1,0,0,0,0.000000," ","integrate(x^3*(a+b*tan(d*x^2+c)),x, algorithm=""maxima"")","\frac{1}{4} \, a x^{4} + 2 \, b \int \frac{x^{3} \sin\left(2 \, d x^{2} + 2 \, c\right)}{\cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x^{2} + 2 \, c\right) + 1}\,{d x}"," ",0,"1/4*a*x^4 + 2*b*integrate(x^3*sin(2*d*x^2 + 2*c)/(cos(2*d*x^2 + 2*c)^2 + sin(2*d*x^2 + 2*c)^2 + 2*cos(2*d*x^2 + 2*c) + 1), x)","F",0
2,0,0,0,0.000000," ","integrate(x^2*(a+b*tan(d*x^2+c)),x, algorithm=""maxima"")","\frac{1}{3} \, a x^{3} + 2 \, b \int \frac{x^{2} \sin\left(2 \, d x^{2} + 2 \, c\right)}{\cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x^{2} + 2 \, c\right) + 1}\,{d x}"," ",0,"1/3*a*x^3 + 2*b*integrate(x^2*sin(2*d*x^2 + 2*c)/(cos(2*d*x^2 + 2*c)^2 + sin(2*d*x^2 + 2*c)^2 + 2*cos(2*d*x^2 + 2*c) + 1), x)","F",0
3,1,22,0,0.548431," ","integrate(x*(a+b*tan(d*x^2+c)),x, algorithm=""maxima"")","\frac{1}{2} \, a x^{2} + \frac{b \log\left(\sec\left(d x^{2} + c\right)\right)}{2 \, d}"," ",0,"1/2*a*x^2 + 1/2*b*log(sec(d*x^2 + c))/d","A",0
4,0,0,0,0.000000," ","integrate(a+b*tan(d*x^2+c),x, algorithm=""maxima"")","a x + 2 \, b \int \frac{\sin\left(2 \, d x^{2} + 2 \, c\right)}{\cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x^{2} + 2 \, c\right) + 1}\,{d x}"," ",0,"a*x + 2*b*integrate(sin(2*d*x^2 + 2*c)/(cos(2*d*x^2 + 2*c)^2 + sin(2*d*x^2 + 2*c)^2 + 2*cos(2*d*x^2 + 2*c) + 1), x)","F",0
5,0,0,0,0.000000," ","integrate((a+b*tan(d*x^2+c))/x,x, algorithm=""maxima"")","2 \, b \int \frac{\sin\left(2 \, d x^{2} + 2 \, c\right)}{x \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + x \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, x \cos\left(2 \, d x^{2} + 2 \, c\right) + x}\,{d x} + a \log\left(x\right)"," ",0,"2*b*integrate(sin(2*d*x^2 + 2*c)/(x*cos(2*d*x^2 + 2*c)^2 + x*sin(2*d*x^2 + 2*c)^2 + 2*x*cos(2*d*x^2 + 2*c) + x), x) + a*log(x)","F",0
6,0,0,0,0.000000," ","integrate((a+b*tan(d*x^2+c))/x^2,x, algorithm=""maxima"")","2 \, b \int \frac{\sin\left(2 \, d x^{2} + 2 \, c\right)}{x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + x^{2} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right) + x^{2}}\,{d x} - \frac{a}{x}"," ",0,"2*b*integrate(sin(2*d*x^2 + 2*c)/(x^2*cos(2*d*x^2 + 2*c)^2 + x^2*sin(2*d*x^2 + 2*c)^2 + 2*x^2*cos(2*d*x^2 + 2*c) + x^2), x) - a/x","F",0
7,1,398,0,1.667806," ","integrate(x^3*(a+b*tan(d*x^2+c))^2,x, algorithm=""maxima"")","\frac{1}{4} \, a^{2} x^{4} + \frac{{\left(2 \, a b + i \, b^{2}\right)} d^{2} x^{4} - {\left(4 \, a b d x^{2} - 2 \, b^{2} + 2 \, {\left(2 \, a b d x^{2} - b^{2}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right) + {\left(4 i \, a b d x^{2} - 2 i \, b^{2}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)\right)} \arctan\left(\sin\left(2 \, d x^{2} + 2 \, c\right), \cos\left(2 \, d x^{2} + 2 \, c\right) + 1\right) + {\left({\left(2 \, a b + i \, b^{2}\right)} d^{2} x^{4} - 4 \, b^{2} d x^{2}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right) + 2 \, {\left(a b \cos\left(2 \, d x^{2} + 2 \, c\right) + i \, a b \sin\left(2 \, d x^{2} + 2 \, c\right) + a b\right)} {\rm Li}_2\left(-e^{\left(2 i \, d x^{2} + 2 i \, c\right)}\right) - {\left(-2 i \, a b d x^{2} + i \, b^{2} + {\left(-2 i \, a b d x^{2} + i \, b^{2}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right) + {\left(2 \, a b d x^{2} - b^{2}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)\right)} \log\left(\cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x^{2} + 2 \, c\right) + 1\right) - {\left({\left(-2 i \, a b + b^{2}\right)} d^{2} x^{4} + 4 i \, b^{2} d x^{2}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)}{-4 i \, d^{2} \cos\left(2 \, d x^{2} + 2 \, c\right) + 4 \, d^{2} \sin\left(2 \, d x^{2} + 2 \, c\right) - 4 i \, d^{2}}"," ",0,"1/4*a^2*x^4 + ((2*a*b + I*b^2)*d^2*x^4 - (4*a*b*d*x^2 - 2*b^2 + 2*(2*a*b*d*x^2 - b^2)*cos(2*d*x^2 + 2*c) + (4*I*a*b*d*x^2 - 2*I*b^2)*sin(2*d*x^2 + 2*c))*arctan2(sin(2*d*x^2 + 2*c), cos(2*d*x^2 + 2*c) + 1) + ((2*a*b + I*b^2)*d^2*x^4 - 4*b^2*d*x^2)*cos(2*d*x^2 + 2*c) + 2*(a*b*cos(2*d*x^2 + 2*c) + I*a*b*sin(2*d*x^2 + 2*c) + a*b)*dilog(-e^(2*I*d*x^2 + 2*I*c)) - (-2*I*a*b*d*x^2 + I*b^2 + (-2*I*a*b*d*x^2 + I*b^2)*cos(2*d*x^2 + 2*c) + (2*a*b*d*x^2 - b^2)*sin(2*d*x^2 + 2*c))*log(cos(2*d*x^2 + 2*c)^2 + sin(2*d*x^2 + 2*c)^2 + 2*cos(2*d*x^2 + 2*c) + 1) - ((-2*I*a*b + b^2)*d^2*x^4 + 4*I*b^2*d*x^2)*sin(2*d*x^2 + 2*c))/(-4*I*d^2*cos(2*d*x^2 + 2*c) + 4*d^2*sin(2*d*x^2 + 2*c) - 4*I*d^2)","B",0
8,0,0,0,0.000000," ","integrate(x^2*(a+b*tan(d*x^2+c))^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} x^{3} - \frac{b^{2} d x^{3} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + b^{2} d x^{3} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, b^{2} d x^{3} \cos\left(2 \, d x^{2} + 2 \, c\right) + b^{2} d x^{3} - 3 \, b^{2} x \sin\left(2 \, d x^{2} + 2 \, c\right) - \frac{3 \, {\left(d \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d x^{2} + 2 \, c\right) + d\right)} {\left(4 \, a d \int \frac{x^{2} \sin\left(2 \, d x^{2} + 2 \, c\right)}{\cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x^{2} + 2 \, c\right) + 1}\,{d x} - b \int \frac{\sin\left(2 \, d x^{2} + 2 \, c\right)}{\cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x^{2} + 2 \, c\right) + 1}\,{d x}\right)} b}{d}}{3 \, {\left(d \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d x^{2} + 2 \, c\right) + d\right)}}"," ",0,"1/3*a^2*x^3 - 1/3*(b^2*d*x^3*cos(2*d*x^2 + 2*c)^2 + b^2*d*x^3*sin(2*d*x^2 + 2*c)^2 + 2*b^2*d*x^3*cos(2*d*x^2 + 2*c) + b^2*d*x^3 - 3*b^2*x*sin(2*d*x^2 + 2*c) - 3*(d*cos(2*d*x^2 + 2*c)^2 + d*sin(2*d*x^2 + 2*c)^2 + 2*d*cos(2*d*x^2 + 2*c) + d)*integrate((4*a*b*d*x^2 - b^2)*sin(2*d*x^2 + 2*c)/(d*cos(2*d*x^2 + 2*c)^2 + d*sin(2*d*x^2 + 2*c)^2 + 2*d*cos(2*d*x^2 + 2*c) + d), x))/(d*cos(2*d*x^2 + 2*c)^2 + d*sin(2*d*x^2 + 2*c)^2 + 2*d*cos(2*d*x^2 + 2*c) + d)","F",0
9,1,149,0,0.429819," ","integrate(x*(a+b*tan(d*x^2+c))^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} x^{2} - \frac{{\left(d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d x^{2} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right) + d x^{2} - 2 \, \sin\left(2 \, d x^{2} + 2 \, c\right)\right)} b^{2}}{2 \, {\left(d \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d x^{2} + 2 \, c\right) + d\right)}} + \frac{a b \log\left(\sec\left(d x^{2} + c\right)\right)}{d}"," ",0,"1/2*a^2*x^2 - 1/2*(d*x^2*cos(2*d*x^2 + 2*c)^2 + d*x^2*sin(2*d*x^2 + 2*c)^2 + 2*d*x^2*cos(2*d*x^2 + 2*c) + d*x^2 - 2*sin(2*d*x^2 + 2*c))*b^2/(d*cos(2*d*x^2 + 2*c)^2 + d*sin(2*d*x^2 + 2*c)^2 + 2*d*cos(2*d*x^2 + 2*c) + d) + a*b*log(sec(d*x^2 + c))/d","B",0
10,0,0,0,0.000000," ","integrate((a+b*tan(d*x^2+c))^2,x, algorithm=""maxima"")","a^{2} x - \frac{b^{2} d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + b^{2} d x^{2} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, b^{2} d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right) + b^{2} d x^{2} - b^{2} \sin\left(2 \, d x^{2} + 2 \, c\right) - \frac{{\left(d x \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d x \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, d x \cos\left(2 \, d x^{2} + 2 \, c\right) + d x\right)} {\left(4 \, a d \int \frac{x^{2} \sin\left(2 \, d x^{2} + 2 \, c\right)}{x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + x^{2} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right) + x^{2}}\,{d x} + b \int \frac{\sin\left(2 \, d x^{2} + 2 \, c\right)}{x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + x^{2} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right) + x^{2}}\,{d x}\right)} b}{d}}{d x \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d x \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, d x \cos\left(2 \, d x^{2} + 2 \, c\right) + d x}"," ",0,"a^2*x - (b^2*d*x^2*cos(2*d*x^2 + 2*c)^2 + b^2*d*x^2*sin(2*d*x^2 + 2*c)^2 + 2*b^2*d*x^2*cos(2*d*x^2 + 2*c) + b^2*d*x^2 - b^2*sin(2*d*x^2 + 2*c) - (d*x*cos(2*d*x^2 + 2*c)^2 + d*x*sin(2*d*x^2 + 2*c)^2 + 2*d*x*cos(2*d*x^2 + 2*c) + d*x)*integrate((4*a*b*d*x^2 + b^2)*sin(2*d*x^2 + 2*c)/(d*x^2*cos(2*d*x^2 + 2*c)^2 + d*x^2*sin(2*d*x^2 + 2*c)^2 + 2*d*x^2*cos(2*d*x^2 + 2*c) + d*x^2), x))/(d*x*cos(2*d*x^2 + 2*c)^2 + d*x*sin(2*d*x^2 + 2*c)^2 + 2*d*x*cos(2*d*x^2 + 2*c) + d*x)","F",0
11,0,0,0,0.000000," ","integrate((a+b*tan(d*x^2+c))^2/x,x, algorithm=""maxima"")","a^{2} \log\left(x\right) - \frac{b^{2} d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} \log\left(x\right) + b^{2} d x^{2} \log\left(x\right) \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, b^{2} d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right) \log\left(x\right) + b^{2} d x^{2} \log\left(x\right) - b^{2} \sin\left(2 \, d x^{2} + 2 \, c\right) - 2 \, {\left(d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d x^{2} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right) + d x^{2}\right)} \int \frac{{\left(2 \, a b d x^{2} + b^{2}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)}{d x^{3} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d x^{3} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, d x^{3} \cos\left(2 \, d x^{2} + 2 \, c\right) + d x^{3}}\,{d x}}{d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d x^{2} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right) + d x^{2}}"," ",0,"a^2*log(x) - (b^2*d*x^2*cos(2*d*x^2 + 2*c)^2*log(x) + b^2*d*x^2*log(x)*sin(2*d*x^2 + 2*c)^2 + 2*b^2*d*x^2*cos(2*d*x^2 + 2*c)*log(x) + b^2*d*x^2*log(x) - b^2*sin(2*d*x^2 + 2*c) - (d*x^2*cos(2*d*x^2 + 2*c)^2 + d*x^2*sin(2*d*x^2 + 2*c)^2 + 2*d*x^2*cos(2*d*x^2 + 2*c) + d*x^2)*integrate(2*(2*a*b*d*x^2 + b^2)*sin(2*d*x^2 + 2*c)/(d*x^3*cos(2*d*x^2 + 2*c)^2 + d*x^3*sin(2*d*x^2 + 2*c)^2 + 2*d*x^3*cos(2*d*x^2 + 2*c) + d*x^3), x))/(d*x^2*cos(2*d*x^2 + 2*c)^2 + d*x^2*sin(2*d*x^2 + 2*c)^2 + 2*d*x^2*cos(2*d*x^2 + 2*c) + d*x^2)","F",0
12,0,0,0,0.000000," ","integrate((a+b*tan(d*x^2+c))^2/x^2,x, algorithm=""maxima"")","-\frac{a^{2}}{x} + \frac{b^{2} d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + b^{2} d x^{2} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, b^{2} d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right) + b^{2} d x^{2} + b^{2} \sin\left(2 \, d x^{2} + 2 \, c\right) + \frac{{\left(d x^{3} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d x^{3} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, d x^{3} \cos\left(2 \, d x^{2} + 2 \, c\right) + d x^{3}\right)} {\left(4 \, a d \int \frac{x^{2} \sin\left(2 \, d x^{2} + 2 \, c\right)}{x^{4} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + x^{4} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, x^{4} \cos\left(2 \, d x^{2} + 2 \, c\right) + x^{4}}\,{d x} + 3 \, b \int \frac{\sin\left(2 \, d x^{2} + 2 \, c\right)}{x^{4} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + x^{4} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, x^{4} \cos\left(2 \, d x^{2} + 2 \, c\right) + x^{4}}\,{d x}\right)} b}{d}}{d x^{3} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d x^{3} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, d x^{3} \cos\left(2 \, d x^{2} + 2 \, c\right) + d x^{3}}"," ",0,"-a^2/x + (b^2*d*x^2*cos(2*d*x^2 + 2*c)^2 + b^2*d*x^2*sin(2*d*x^2 + 2*c)^2 + 2*b^2*d*x^2*cos(2*d*x^2 + 2*c) + b^2*d*x^2 + b^2*sin(2*d*x^2 + 2*c) + (d*x^3*cos(2*d*x^2 + 2*c)^2 + d*x^3*sin(2*d*x^2 + 2*c)^2 + 2*d*x^3*cos(2*d*x^2 + 2*c) + d*x^3)*integrate((4*a*b*d*x^2 + 3*b^2)*sin(2*d*x^2 + 2*c)/(d*x^4*cos(2*d*x^2 + 2*c)^2 + d*x^4*sin(2*d*x^2 + 2*c)^2 + 2*d*x^4*cos(2*d*x^2 + 2*c) + d*x^4), x))/(d*x^3*cos(2*d*x^2 + 2*c)^2 + d*x^3*sin(2*d*x^2 + 2*c)^2 + 2*d*x^3*cos(2*d*x^2 + 2*c) + d*x^3)","F",0
13,1,267,0,0.822509," ","integrate(x^3/(a+b*tan(d*x^2+c)),x, algorithm=""maxima"")","\frac{{\left(a - i \, b\right)} d^{2} x^{4} - 2 i \, b d x^{2} \arctan\left(\frac{2 \, a b \cos\left(2 \, d x^{2} + 2 \, c\right) - {\left(a^{2} - b^{2}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)}{a^{2} + b^{2}}, \frac{2 \, a b \sin\left(2 \, d x^{2} + 2 \, c\right) + a^{2} + b^{2} + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right)}{a^{2} + b^{2}}\right) + b d x^{2} \log\left(\frac{{\left(a^{2} + b^{2}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + 4 \, a b \sin\left(2 \, d x^{2} + 2 \, c\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right)}{a^{2} + b^{2}}\right) - i \, b {\rm Li}_2\left(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{2} + 2 i \, c\right)}}{-i \, a + b}\right)}{4 \, {\left(a^{2} + b^{2}\right)} d^{2}}"," ",0,"1/4*((a - I*b)*d^2*x^4 - 2*I*b*d*x^2*arctan2((2*a*b*cos(2*d*x^2 + 2*c) - (a^2 - b^2)*sin(2*d*x^2 + 2*c))/(a^2 + b^2), (2*a*b*sin(2*d*x^2 + 2*c) + a^2 + b^2 + (a^2 - b^2)*cos(2*d*x^2 + 2*c))/(a^2 + b^2)) + b*d*x^2*log(((a^2 + b^2)*cos(2*d*x^2 + 2*c)^2 + 4*a*b*sin(2*d*x^2 + 2*c) + (a^2 + b^2)*sin(2*d*x^2 + 2*c)^2 + a^2 + b^2 + 2*(a^2 - b^2)*cos(2*d*x^2 + 2*c))/(a^2 + b^2)) - I*b*dilog((I*a + b)*e^(2*I*d*x^2 + 2*I*c)/(-I*a + b)))/((a^2 + b^2)*d^2)","B",0
14,-1,0,0,0.000000," ","integrate(x^2/(a+b*tan(d*x^2+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
15,1,143,0,0.985533," ","integrate(x/(a+b*tan(d*x^2+c)),x, algorithm=""maxima"")","\frac{2 \, a d x^{2} + b \log\left(\frac{{\left(a^{2} + b^{2}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + 4 \, a b \sin\left(2 \, d x^{2} + 2 \, c\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, c\right)^{2}}\right)}{4 \, {\left(a^{2} + b^{2}\right)} d}"," ",0,"1/4*(2*a*d*x^2 + b*log(((a^2 + b^2)*cos(2*d*x^2 + 2*c)^2 + 4*a*b*sin(2*d*x^2 + 2*c) + (a^2 + b^2)*sin(2*d*x^2 + 2*c)^2 + a^2 + b^2 + 2*(a^2 - b^2)*cos(2*d*x^2 + 2*c))/((a^2 + b^2)*cos(2*c)^2 + (a^2 + b^2)*sin(2*c)^2)))/((a^2 + b^2)*d)","B",0
16,-1,0,0,0.000000," ","integrate(1/(a+b*tan(d*x^2+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
17,-1,0,0,0.000000," ","integrate(1/x/(a+b*tan(d*x^2+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
18,-1,0,0,0.000000," ","integrate(1/x^2/(a+b*tan(d*x^2+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
19,1,1008,0,1.261064," ","integrate(x^3/(a+b*tan(d*x^2+c))^2,x, algorithm=""maxima"")","\frac{{\left(a^{3} - i \, a^{2} b + a b^{2} - i \, b^{3}\right)} d^{2} x^{4} + {\left(2 i \, a b^{2} - 2 \, b^{3} + {\left(2 i \, a b^{2} + 2 \, b^{3}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right) - 2 \, {\left(a b^{2} - i \, b^{3}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)\right)} \arctan\left(-b \cos\left(2 \, d x^{2} + 2 \, c\right) + a \sin\left(2 \, d x^{2} + 2 \, c\right) + b, a \cos\left(2 \, d x^{2} + 2 \, c\right) + b \sin\left(2 \, d x^{2} + 2 \, c\right) + a\right) + {\left({\left(-4 i \, a^{2} b - 4 \, a b^{2}\right)} d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right) + 4 \, {\left(a^{2} b - i \, a b^{2}\right)} d x^{2} \sin\left(2 \, d x^{2} + 2 \, c\right) + {\left(-4 i \, a^{2} b + 4 \, a b^{2}\right)} d x^{2}\right)} \arctan\left(\frac{2 \, a b \cos\left(2 \, d x^{2} + 2 \, c\right) - {\left(a^{2} - b^{2}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)}{a^{2} + b^{2}}, \frac{2 \, a b \sin\left(2 \, d x^{2} + 2 \, c\right) + a^{2} + b^{2} + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right)}{a^{2} + b^{2}}\right) + {\left({\left(a^{3} - 3 i \, a^{2} b - 3 \, a b^{2} + i \, b^{3}\right)} d^{2} x^{4} + {\left(-4 i \, a b^{2} - 4 \, b^{3}\right)} d x^{2}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right) + {\left(-2 i \, a^{2} b + 2 \, a b^{2} + {\left(-2 i \, a^{2} b - 2 \, a b^{2}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right) + 2 \, {\left(a^{2} b - i \, a b^{2}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)\right)} {\rm Li}_2\left(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{2} + 2 i \, c\right)}}{-i \, a + b}\right) + {\left(a b^{2} + i \, b^{3} + {\left(a b^{2} - i \, b^{3}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right) + {\left(i \, a b^{2} + b^{3}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)\right)} \log\left({\left(a^{2} + b^{2}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + 4 \, a b \sin\left(2 \, d x^{2} + 2 \, c\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right)\right) + {\left(2 \, {\left(a^{2} b - i \, a b^{2}\right)} d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right) + {\left(2 i \, a^{2} b + 2 \, a b^{2}\right)} d x^{2} \sin\left(2 \, d x^{2} + 2 \, c\right) + 2 \, {\left(a^{2} b + i \, a b^{2}\right)} d x^{2}\right)} \log\left(\frac{{\left(a^{2} + b^{2}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + 4 \, a b \sin\left(2 \, d x^{2} + 2 \, c\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right)}{a^{2} + b^{2}}\right) + {\left({\left(i \, a^{3} + 3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} d^{2} x^{4} + 4 \, {\left(a b^{2} - i \, b^{3}\right)} d x^{2}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)}{{\left(4 \, a^{5} - 4 i \, a^{4} b + 8 \, a^{3} b^{2} - 8 i \, a^{2} b^{3} + 4 \, a b^{4} - 4 i \, b^{5}\right)} d^{2} \cos\left(2 \, d x^{2} + 2 \, c\right) + {\left(4 i \, a^{5} + 4 \, a^{4} b + 8 i \, a^{3} b^{2} + 8 \, a^{2} b^{3} + 4 i \, a b^{4} + 4 \, b^{5}\right)} d^{2} \sin\left(2 \, d x^{2} + 2 \, c\right) + {\left(4 \, a^{5} + 4 i \, a^{4} b + 8 \, a^{3} b^{2} + 8 i \, a^{2} b^{3} + 4 \, a b^{4} + 4 i \, b^{5}\right)} d^{2}}"," ",0,"((a^3 - I*a^2*b + a*b^2 - I*b^3)*d^2*x^4 + (2*I*a*b^2 - 2*b^3 + (2*I*a*b^2 + 2*b^3)*cos(2*d*x^2 + 2*c) - 2*(a*b^2 - I*b^3)*sin(2*d*x^2 + 2*c))*arctan2(-b*cos(2*d*x^2 + 2*c) + a*sin(2*d*x^2 + 2*c) + b, a*cos(2*d*x^2 + 2*c) + b*sin(2*d*x^2 + 2*c) + a) + ((-4*I*a^2*b - 4*a*b^2)*d*x^2*cos(2*d*x^2 + 2*c) + 4*(a^2*b - I*a*b^2)*d*x^2*sin(2*d*x^2 + 2*c) + (-4*I*a^2*b + 4*a*b^2)*d*x^2)*arctan2((2*a*b*cos(2*d*x^2 + 2*c) - (a^2 - b^2)*sin(2*d*x^2 + 2*c))/(a^2 + b^2), (2*a*b*sin(2*d*x^2 + 2*c) + a^2 + b^2 + (a^2 - b^2)*cos(2*d*x^2 + 2*c))/(a^2 + b^2)) + ((a^3 - 3*I*a^2*b - 3*a*b^2 + I*b^3)*d^2*x^4 + (-4*I*a*b^2 - 4*b^3)*d*x^2)*cos(2*d*x^2 + 2*c) + (-2*I*a^2*b + 2*a*b^2 + (-2*I*a^2*b - 2*a*b^2)*cos(2*d*x^2 + 2*c) + 2*(a^2*b - I*a*b^2)*sin(2*d*x^2 + 2*c))*dilog((I*a + b)*e^(2*I*d*x^2 + 2*I*c)/(-I*a + b)) + (a*b^2 + I*b^3 + (a*b^2 - I*b^3)*cos(2*d*x^2 + 2*c) + (I*a*b^2 + b^3)*sin(2*d*x^2 + 2*c))*log((a^2 + b^2)*cos(2*d*x^2 + 2*c)^2 + 4*a*b*sin(2*d*x^2 + 2*c) + (a^2 + b^2)*sin(2*d*x^2 + 2*c)^2 + a^2 + b^2 + 2*(a^2 - b^2)*cos(2*d*x^2 + 2*c)) + (2*(a^2*b - I*a*b^2)*d*x^2*cos(2*d*x^2 + 2*c) + (2*I*a^2*b + 2*a*b^2)*d*x^2*sin(2*d*x^2 + 2*c) + 2*(a^2*b + I*a*b^2)*d*x^2)*log(((a^2 + b^2)*cos(2*d*x^2 + 2*c)^2 + 4*a*b*sin(2*d*x^2 + 2*c) + (a^2 + b^2)*sin(2*d*x^2 + 2*c)^2 + a^2 + b^2 + 2*(a^2 - b^2)*cos(2*d*x^2 + 2*c))/(a^2 + b^2)) + ((I*a^3 + 3*a^2*b - 3*I*a*b^2 - b^3)*d^2*x^4 + 4*(a*b^2 - I*b^3)*d*x^2)*sin(2*d*x^2 + 2*c))/((4*a^5 - 4*I*a^4*b + 8*a^3*b^2 - 8*I*a^2*b^3 + 4*a*b^4 - 4*I*b^5)*d^2*cos(2*d*x^2 + 2*c) + (4*I*a^5 + 4*a^4*b + 8*I*a^3*b^2 + 8*a^2*b^3 + 4*I*a*b^4 + 4*b^5)*d^2*sin(2*d*x^2 + 2*c) + (4*a^5 + 4*I*a^4*b + 8*a^3*b^2 + 8*I*a^2*b^3 + 4*a*b^4 + 4*I*b^5)*d^2)","B",0
20,-1,0,0,0.000000," ","integrate(x^2/(a+b*tan(d*x^2+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
21,1,556,0,1.409231," ","integrate(x/(a+b*tan(d*x^2+c))^2,x, algorithm=""maxima"")","\frac{{\left(a^{4} - b^{4}\right)} d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + {\left(a^{4} - b^{4}\right)} d x^{2} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + {\left(a^{4} - b^{4}\right)} d x^{2} - 2 \, {\left(2 \, a b^{3} - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d x^{2}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right) + {\left(4 \, a^{2} b^{2} \sin\left(2 \, d x^{2} + 2 \, c\right) + a^{3} b + a b^{3} + {\left(a^{3} b + a b^{3}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + {\left(a^{3} b + a b^{3}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right)\right)} \log\left(\frac{{\left(a^{2} + b^{2}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + 4 \, a b \sin\left(2 \, d x^{2} + 2 \, c\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(2 \, c\right)^{2} + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, c\right)^{2}}\right) + 2 \, {\left(a^{2} b^{2} - b^{4} + 2 \, {\left(a^{3} b - a b^{3}\right)} d x^{2}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)}{2 \, {\left({\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, {\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} d \cos\left(2 \, d x^{2} + 2 \, c\right) + 4 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d \sin\left(2 \, d x^{2} + 2 \, c\right) + {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d\right)}}"," ",0,"1/2*((a^4 - b^4)*d*x^2*cos(2*d*x^2 + 2*c)^2 + (a^4 - b^4)*d*x^2*sin(2*d*x^2 + 2*c)^2 + (a^4 - b^4)*d*x^2 - 2*(2*a*b^3 - (a^4 - 2*a^2*b^2 + b^4)*d*x^2)*cos(2*d*x^2 + 2*c) + (4*a^2*b^2*sin(2*d*x^2 + 2*c) + a^3*b + a*b^3 + (a^3*b + a*b^3)*cos(2*d*x^2 + 2*c)^2 + (a^3*b + a*b^3)*sin(2*d*x^2 + 2*c)^2 + 2*(a^3*b - a*b^3)*cos(2*d*x^2 + 2*c))*log(((a^2 + b^2)*cos(2*d*x^2 + 2*c)^2 + 4*a*b*sin(2*d*x^2 + 2*c) + (a^2 + b^2)*sin(2*d*x^2 + 2*c)^2 + a^2 + b^2 + 2*(a^2 - b^2)*cos(2*d*x^2 + 2*c))/((a^2 + b^2)*cos(2*c)^2 + (a^2 + b^2)*sin(2*c)^2)) + 2*(a^2*b^2 - b^4 + 2*(a^3*b - a*b^3)*d*x^2)*sin(2*d*x^2 + 2*c))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d*cos(2*d*x^2 + 2*c)^2 + (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d*sin(2*d*x^2 + 2*c)^2 + 2*(a^6 + a^4*b^2 - a^2*b^4 - b^6)*d*cos(2*d*x^2 + 2*c) + 4*(a^5*b + 2*a^3*b^3 + a*b^5)*d*sin(2*d*x^2 + 2*c) + (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d)","B",0
22,-1,0,0,0.000000," ","integrate(1/(a+b*tan(d*x^2+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
23,0,0,0,0.000000," ","integrate(1/x/(a+b*tan(d*x^2+c))^2,x, algorithm=""maxima"")","\frac{{\left({\left(4 \, a^{8} b^{2} + 4 \, a^{6} b^{4} - 4 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} \cos\left(2 \, c\right)^{2} + {\left(4 \, a^{8} b^{2} + 4 \, a^{6} b^{4} - 4 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{2} \cos\left(2 \, d x^{2}\right)^{2} \log\left(x\right) + {\left(a^{10} - a^{8} b^{2}\right)} d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} \log\left(x\right) + {\left({\left(4 \, a^{8} b^{2} + 4 \, a^{6} b^{4} - 4 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} \cos\left(2 \, c\right)^{2} + {\left(4 \, a^{8} b^{2} + 4 \, a^{6} b^{4} - 4 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{2} \log\left(x\right) \sin\left(2 \, d x^{2}\right)^{2} + {\left(a^{10} - a^{8} b^{2}\right)} d x^{2} \log\left(x\right) \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + {\left(a^{10} + 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} d x^{2} \log\left(x\right) - {\left(2 \, {\left({\left(a^{6} b^{4} + a^{4} b^{6} - a^{2} b^{8} - b^{10}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{9} b + 2 \, a^{7} b^{3} - 2 \, a^{3} b^{7} - a b^{9}\right)} \sin\left(2 \, c\right)\right)} d x^{2} \log\left(x\right) + 2 \, {\left(a^{7} b^{3} + 3 \, a^{5} b^{5} + 3 \, a^{3} b^{7} + a b^{9}\right)} \cos\left(2 \, c\right) + {\left(a^{4} b^{6} + 2 \, a^{2} b^{8} + b^{10}\right)} \sin\left(2 \, c\right)\right)} \cos\left(2 \, d x^{2}\right) - 2 \, {\left({\left({\left(a^{6} b^{4} - a^{4} b^{6}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{9} b - a^{5} b^{5}\right)} \sin\left(2 \, c\right)\right)} d x^{2} \cos\left(2 \, d x^{2}\right) \log\left(x\right) - {\left(2 \, {\left(a^{9} b - a^{5} b^{5}\right)} \cos\left(2 \, c\right) + {\left(a^{6} b^{4} - a^{4} b^{6}\right)} \sin\left(2 \, c\right)\right)} d x^{2} \log\left(x\right) \sin\left(2 \, d x^{2}\right) - {\left(a^{10} + a^{8} b^{2} - a^{6} b^{4} - a^{4} b^{6}\right)} d x^{2} \log\left(x\right)\right)} \cos\left(2 \, d x^{2} + 2 \, c\right) - 2 \, {\left({\left({\left(4 \, a^{10} b^{2} + 16 \, a^{8} b^{4} + 24 \, a^{6} b^{6} + 17 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} \cos\left(2 \, c\right)^{2} + {\left(4 \, a^{10} b^{2} + 16 \, a^{8} b^{4} + 24 \, a^{6} b^{6} + 17 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{2} \cos\left(2 \, d x^{2}\right)^{2} + {\left(a^{12} + 2 \, a^{10} b^{2} + a^{8} b^{4}\right)} d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + {\left({\left(4 \, a^{10} b^{2} + 16 \, a^{8} b^{4} + 24 \, a^{6} b^{6} + 17 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} \cos\left(2 \, c\right)^{2} + {\left(4 \, a^{10} b^{2} + 16 \, a^{8} b^{4} + 24 \, a^{6} b^{6} + 17 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{2} \sin\left(2 \, d x^{2}\right)^{2} + {\left(a^{12} + 2 \, a^{10} b^{2} + a^{8} b^{4}\right)} d x^{2} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} - 2 \, {\left({\left(a^{8} b^{4} + 4 \, a^{6} b^{6} + 6 \, a^{4} b^{8} + 4 \, a^{2} b^{10} + b^{12}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{11} b + 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} + 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} + a b^{11}\right)} \sin\left(2 \, c\right)\right)} d x^{2} \cos\left(2 \, d x^{2}\right) + 2 \, {\left(2 \, {\left(a^{11} b + 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} + 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} + a b^{11}\right)} \cos\left(2 \, c\right) + {\left(a^{8} b^{4} + 4 \, a^{6} b^{6} + 6 \, a^{4} b^{8} + 4 \, a^{2} b^{10} + b^{12}\right)} \sin\left(2 \, c\right)\right)} d x^{2} \sin\left(2 \, d x^{2}\right) + {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d x^{2} - 2 \, {\left({\left({\left(a^{8} b^{4} + 2 \, a^{6} b^{6} + a^{4} b^{8}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} \sin\left(2 \, c\right)\right)} d x^{2} \cos\left(2 \, d x^{2}\right) - {\left(2 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} \cos\left(2 \, c\right) + {\left(a^{8} b^{4} + 2 \, a^{6} b^{6} + a^{4} b^{8}\right)} \sin\left(2 \, c\right)\right)} d x^{2} \sin\left(2 \, d x^{2}\right) - {\left(a^{12} + 4 \, a^{10} b^{2} + 6 \, a^{8} b^{4} + 4 \, a^{6} b^{6} + a^{4} b^{8}\right)} d x^{2}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right) - 2 \, {\left({\left(2 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} \cos\left(2 \, c\right) + {\left(a^{8} b^{4} + 2 \, a^{6} b^{6} + a^{4} b^{8}\right)} \sin\left(2 \, c\right)\right)} d x^{2} \cos\left(2 \, d x^{2}\right) + {\left({\left(a^{8} b^{4} + 2 \, a^{6} b^{6} + a^{4} b^{8}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} \sin\left(2 \, c\right)\right)} d x^{2} \sin\left(2 \, d x^{2}\right)\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)\right)} \int \frac{{\left(b^{6} \sin\left(2 \, c\right) - 2 \, {\left(a b^{5} \sin\left(2 \, c\right) + 2 \, {\left(a^{4} b^{2} + a^{2} b^{4}\right)} \cos\left(2 \, c\right)\right)} d x^{2} + 2 \, {\left(a^{3} b^{3} + a b^{5}\right)} \cos\left(2 \, c\right)\right)} \cos\left(2 \, d x^{2}\right) + {\left(b^{6} \cos\left(2 \, c\right) - 2 \, {\left(a b^{5} \cos\left(2 \, c\right) - 2 \, {\left(a^{4} b^{2} + a^{2} b^{4}\right)} \sin\left(2 \, c\right)\right)} d x^{2} - 2 \, {\left(a^{3} b^{3} + a b^{5}\right)} \sin\left(2 \, c\right)\right)} \sin\left(2 \, d x^{2}\right) + {\left(2 \, a^{5} b d x^{2} - a^{4} b^{2}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)}{a^{8} d x^{3} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + a^{8} d x^{3} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + {\left({\left(4 \, a^{6} b^{2} + 8 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} \cos\left(2 \, c\right)^{2} + {\left(4 \, a^{6} b^{2} + 8 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{3} \cos\left(2 \, d x^{2}\right)^{2} + {\left({\left(4 \, a^{6} b^{2} + 8 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} \cos\left(2 \, c\right)^{2} + {\left(4 \, a^{6} b^{2} + 8 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{3} \sin\left(2 \, d x^{2}\right)^{2} - 2 \, {\left({\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} \sin\left(2 \, c\right)\right)} d x^{3} \cos\left(2 \, d x^{2}\right) + 2 \, {\left(2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} \cos\left(2 \, c\right) + {\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} \sin\left(2 \, c\right)\right)} d x^{3} \sin\left(2 \, d x^{2}\right) + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d x^{3} - 2 \, {\left({\left(a^{4} b^{4} \cos\left(2 \, c\right) - 2 \, {\left(a^{7} b + a^{5} b^{3}\right)} \sin\left(2 \, c\right)\right)} d x^{3} \cos\left(2 \, d x^{2}\right) - {\left(a^{4} b^{4} \sin\left(2 \, c\right) + 2 \, {\left(a^{7} b + a^{5} b^{3}\right)} \cos\left(2 \, c\right)\right)} d x^{3} \sin\left(2 \, d x^{2}\right) - {\left(a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} d x^{3}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right) - 2 \, {\left({\left(a^{4} b^{4} \sin\left(2 \, c\right) + 2 \, {\left(a^{7} b + a^{5} b^{3}\right)} \cos\left(2 \, c\right)\right)} d x^{3} \cos\left(2 \, d x^{2}\right) + {\left(a^{4} b^{4} \cos\left(2 \, c\right) - 2 \, {\left(a^{7} b + a^{5} b^{3}\right)} \sin\left(2 \, c\right)\right)} d x^{3} \sin\left(2 \, d x^{2}\right)\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)}\,{d x} + {\left(2 \, {\left(2 \, {\left(a^{9} b + 2 \, a^{7} b^{3} - 2 \, a^{3} b^{7} - a b^{9}\right)} \cos\left(2 \, c\right) + {\left(a^{6} b^{4} + a^{4} b^{6} - a^{2} b^{8} - b^{10}\right)} \sin\left(2 \, c\right)\right)} d x^{2} \log\left(x\right) - {\left(a^{4} b^{6} + 2 \, a^{2} b^{8} + b^{10}\right)} \cos\left(2 \, c\right) + 2 \, {\left(a^{7} b^{3} + 3 \, a^{5} b^{5} + 3 \, a^{3} b^{7} + a b^{9}\right)} \sin\left(2 \, c\right)\right)} \sin\left(2 \, d x^{2}\right) + {\left(a^{8} b^{2} + 2 \, a^{6} b^{4} + a^{4} b^{6} - 2 \, {\left(2 \, {\left(a^{9} b - a^{5} b^{5}\right)} \cos\left(2 \, c\right) + {\left(a^{6} b^{4} - a^{4} b^{6}\right)} \sin\left(2 \, c\right)\right)} d x^{2} \cos\left(2 \, d x^{2}\right) \log\left(x\right) - 2 \, {\left({\left(a^{6} b^{4} - a^{4} b^{6}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{9} b - a^{5} b^{5}\right)} \sin\left(2 \, c\right)\right)} d x^{2} \log\left(x\right) \sin\left(2 \, d x^{2}\right)\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)}{{\left({\left(4 \, a^{10} b^{2} + 16 \, a^{8} b^{4} + 24 \, a^{6} b^{6} + 17 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} \cos\left(2 \, c\right)^{2} + {\left(4 \, a^{10} b^{2} + 16 \, a^{8} b^{4} + 24 \, a^{6} b^{6} + 17 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{2} \cos\left(2 \, d x^{2}\right)^{2} + {\left(a^{12} + 2 \, a^{10} b^{2} + a^{8} b^{4}\right)} d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + {\left({\left(4 \, a^{10} b^{2} + 16 \, a^{8} b^{4} + 24 \, a^{6} b^{6} + 17 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} \cos\left(2 \, c\right)^{2} + {\left(4 \, a^{10} b^{2} + 16 \, a^{8} b^{4} + 24 \, a^{6} b^{6} + 17 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} \sin\left(2 \, c\right)^{2}\right)} d x^{2} \sin\left(2 \, d x^{2}\right)^{2} + {\left(a^{12} + 2 \, a^{10} b^{2} + a^{8} b^{4}\right)} d x^{2} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} - 2 \, {\left({\left(a^{8} b^{4} + 4 \, a^{6} b^{6} + 6 \, a^{4} b^{8} + 4 \, a^{2} b^{10} + b^{12}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{11} b + 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} + 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} + a b^{11}\right)} \sin\left(2 \, c\right)\right)} d x^{2} \cos\left(2 \, d x^{2}\right) + 2 \, {\left(2 \, {\left(a^{11} b + 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} + 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} + a b^{11}\right)} \cos\left(2 \, c\right) + {\left(a^{8} b^{4} + 4 \, a^{6} b^{6} + 6 \, a^{4} b^{8} + 4 \, a^{2} b^{10} + b^{12}\right)} \sin\left(2 \, c\right)\right)} d x^{2} \sin\left(2 \, d x^{2}\right) + {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d x^{2} - 2 \, {\left({\left({\left(a^{8} b^{4} + 2 \, a^{6} b^{6} + a^{4} b^{8}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} \sin\left(2 \, c\right)\right)} d x^{2} \cos\left(2 \, d x^{2}\right) - {\left(2 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} \cos\left(2 \, c\right) + {\left(a^{8} b^{4} + 2 \, a^{6} b^{6} + a^{4} b^{8}\right)} \sin\left(2 \, c\right)\right)} d x^{2} \sin\left(2 \, d x^{2}\right) - {\left(a^{12} + 4 \, a^{10} b^{2} + 6 \, a^{8} b^{4} + 4 \, a^{6} b^{6} + a^{4} b^{8}\right)} d x^{2}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right) - 2 \, {\left({\left(2 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} \cos\left(2 \, c\right) + {\left(a^{8} b^{4} + 2 \, a^{6} b^{6} + a^{4} b^{8}\right)} \sin\left(2 \, c\right)\right)} d x^{2} \cos\left(2 \, d x^{2}\right) + {\left({\left(a^{8} b^{4} + 2 \, a^{6} b^{6} + a^{4} b^{8}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} \sin\left(2 \, c\right)\right)} d x^{2} \sin\left(2 \, d x^{2}\right)\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)}"," ",0,"(((4*a^8*b^2 + 4*a^6*b^4 - 4*a^4*b^6 - 3*a^2*b^8 - b^10)*cos(2*c)^2 + (4*a^8*b^2 + 4*a^6*b^4 - 4*a^4*b^6 - 3*a^2*b^8 - b^10)*sin(2*c)^2)*d*x^2*cos(2*d*x^2)^2*log(x) + (a^10 - a^8*b^2)*d*x^2*cos(2*d*x^2 + 2*c)^2*log(x) + ((4*a^8*b^2 + 4*a^6*b^4 - 4*a^4*b^6 - 3*a^2*b^8 - b^10)*cos(2*c)^2 + (4*a^8*b^2 + 4*a^6*b^4 - 4*a^4*b^6 - 3*a^2*b^8 - b^10)*sin(2*c)^2)*d*x^2*log(x)*sin(2*d*x^2)^2 + (a^10 - a^8*b^2)*d*x^2*log(x)*sin(2*d*x^2 + 2*c)^2 + (a^10 + 3*a^8*b^2 + 2*a^6*b^4 - 2*a^4*b^6 - 3*a^2*b^8 - b^10)*d*x^2*log(x) - (2*((a^6*b^4 + a^4*b^6 - a^2*b^8 - b^10)*cos(2*c) - 2*(a^9*b + 2*a^7*b^3 - 2*a^3*b^7 - a*b^9)*sin(2*c))*d*x^2*log(x) + 2*(a^7*b^3 + 3*a^5*b^5 + 3*a^3*b^7 + a*b^9)*cos(2*c) + (a^4*b^6 + 2*a^2*b^8 + b^10)*sin(2*c))*cos(2*d*x^2) - 2*(((a^6*b^4 - a^4*b^6)*cos(2*c) - 2*(a^9*b - a^5*b^5)*sin(2*c))*d*x^2*cos(2*d*x^2)*log(x) - (2*(a^9*b - a^5*b^5)*cos(2*c) + (a^6*b^4 - a^4*b^6)*sin(2*c))*d*x^2*log(x)*sin(2*d*x^2) - (a^10 + a^8*b^2 - a^6*b^4 - a^4*b^6)*d*x^2*log(x))*cos(2*d*x^2 + 2*c) - (((4*a^10*b^2 + 16*a^8*b^4 + 24*a^6*b^6 + 17*a^4*b^8 + 6*a^2*b^10 + b^12)*cos(2*c)^2 + (4*a^10*b^2 + 16*a^8*b^4 + 24*a^6*b^6 + 17*a^4*b^8 + 6*a^2*b^10 + b^12)*sin(2*c)^2)*d*x^2*cos(2*d*x^2)^2 + (a^12 + 2*a^10*b^2 + a^8*b^4)*d*x^2*cos(2*d*x^2 + 2*c)^2 + ((4*a^10*b^2 + 16*a^8*b^4 + 24*a^6*b^6 + 17*a^4*b^8 + 6*a^2*b^10 + b^12)*cos(2*c)^2 + (4*a^10*b^2 + 16*a^8*b^4 + 24*a^6*b^6 + 17*a^4*b^8 + 6*a^2*b^10 + b^12)*sin(2*c)^2)*d*x^2*sin(2*d*x^2)^2 + (a^12 + 2*a^10*b^2 + a^8*b^4)*d*x^2*sin(2*d*x^2 + 2*c)^2 - 2*((a^8*b^4 + 4*a^6*b^6 + 6*a^4*b^8 + 4*a^2*b^10 + b^12)*cos(2*c) - 2*(a^11*b + 5*a^9*b^3 + 10*a^7*b^5 + 10*a^5*b^7 + 5*a^3*b^9 + a*b^11)*sin(2*c))*d*x^2*cos(2*d*x^2) + 2*(2*(a^11*b + 5*a^9*b^3 + 10*a^7*b^5 + 10*a^5*b^7 + 5*a^3*b^9 + a*b^11)*cos(2*c) + (a^8*b^4 + 4*a^6*b^6 + 6*a^4*b^8 + 4*a^2*b^10 + b^12)*sin(2*c))*d*x^2*sin(2*d*x^2) + (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*x^2 - 2*(((a^8*b^4 + 2*a^6*b^6 + a^4*b^8)*cos(2*c) - 2*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*sin(2*c))*d*x^2*cos(2*d*x^2) - (2*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*cos(2*c) + (a^8*b^4 + 2*a^6*b^6 + a^4*b^8)*sin(2*c))*d*x^2*sin(2*d*x^2) - (a^12 + 4*a^10*b^2 + 6*a^8*b^4 + 4*a^6*b^6 + a^4*b^8)*d*x^2)*cos(2*d*x^2 + 2*c) - 2*((2*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*cos(2*c) + (a^8*b^4 + 2*a^6*b^6 + a^4*b^8)*sin(2*c))*d*x^2*cos(2*d*x^2) + ((a^8*b^4 + 2*a^6*b^6 + a^4*b^8)*cos(2*c) - 2*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*sin(2*c))*d*x^2*sin(2*d*x^2))*sin(2*d*x^2 + 2*c))*integrate(2*((b^6*sin(2*c) - 2*(a*b^5*sin(2*c) + 2*(a^4*b^2 + a^2*b^4)*cos(2*c))*d*x^2 + 2*(a^3*b^3 + a*b^5)*cos(2*c))*cos(2*d*x^2) + (b^6*cos(2*c) - 2*(a*b^5*cos(2*c) - 2*(a^4*b^2 + a^2*b^4)*sin(2*c))*d*x^2 - 2*(a^3*b^3 + a*b^5)*sin(2*c))*sin(2*d*x^2) + (2*a^5*b*d*x^2 - a^4*b^2)*sin(2*d*x^2 + 2*c))/(a^8*d*x^3*cos(2*d*x^2 + 2*c)^2 + a^8*d*x^3*sin(2*d*x^2 + 2*c)^2 + ((4*a^6*b^2 + 8*a^4*b^4 + 4*a^2*b^6 + b^8)*cos(2*c)^2 + (4*a^6*b^2 + 8*a^4*b^4 + 4*a^2*b^6 + b^8)*sin(2*c)^2)*d*x^3*cos(2*d*x^2)^2 + ((4*a^6*b^2 + 8*a^4*b^4 + 4*a^2*b^6 + b^8)*cos(2*c)^2 + (4*a^6*b^2 + 8*a^4*b^4 + 4*a^2*b^6 + b^8)*sin(2*c)^2)*d*x^3*sin(2*d*x^2)^2 - 2*((a^4*b^4 + 2*a^2*b^6 + b^8)*cos(2*c) - 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*sin(2*c))*d*x^3*cos(2*d*x^2) + 2*(2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*cos(2*c) + (a^4*b^4 + 2*a^2*b^6 + b^8)*sin(2*c))*d*x^3*sin(2*d*x^2) + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d*x^3 - 2*((a^4*b^4*cos(2*c) - 2*(a^7*b + a^5*b^3)*sin(2*c))*d*x^3*cos(2*d*x^2) - (a^4*b^4*sin(2*c) + 2*(a^7*b + a^5*b^3)*cos(2*c))*d*x^3*sin(2*d*x^2) - (a^8 + 2*a^6*b^2 + a^4*b^4)*d*x^3)*cos(2*d*x^2 + 2*c) - 2*((a^4*b^4*sin(2*c) + 2*(a^7*b + a^5*b^3)*cos(2*c))*d*x^3*cos(2*d*x^2) + (a^4*b^4*cos(2*c) - 2*(a^7*b + a^5*b^3)*sin(2*c))*d*x^3*sin(2*d*x^2))*sin(2*d*x^2 + 2*c)), x) + (2*(2*(a^9*b + 2*a^7*b^3 - 2*a^3*b^7 - a*b^9)*cos(2*c) + (a^6*b^4 + a^4*b^6 - a^2*b^8 - b^10)*sin(2*c))*d*x^2*log(x) - (a^4*b^6 + 2*a^2*b^8 + b^10)*cos(2*c) + 2*(a^7*b^3 + 3*a^5*b^5 + 3*a^3*b^7 + a*b^9)*sin(2*c))*sin(2*d*x^2) + (a^8*b^2 + 2*a^6*b^4 + a^4*b^6 - 2*(2*(a^9*b - a^5*b^5)*cos(2*c) + (a^6*b^4 - a^4*b^6)*sin(2*c))*d*x^2*cos(2*d*x^2)*log(x) - 2*((a^6*b^4 - a^4*b^6)*cos(2*c) - 2*(a^9*b - a^5*b^5)*sin(2*c))*d*x^2*log(x)*sin(2*d*x^2))*sin(2*d*x^2 + 2*c))/(((4*a^10*b^2 + 16*a^8*b^4 + 24*a^6*b^6 + 17*a^4*b^8 + 6*a^2*b^10 + b^12)*cos(2*c)^2 + (4*a^10*b^2 + 16*a^8*b^4 + 24*a^6*b^6 + 17*a^4*b^8 + 6*a^2*b^10 + b^12)*sin(2*c)^2)*d*x^2*cos(2*d*x^2)^2 + (a^12 + 2*a^10*b^2 + a^8*b^4)*d*x^2*cos(2*d*x^2 + 2*c)^2 + ((4*a^10*b^2 + 16*a^8*b^4 + 24*a^6*b^6 + 17*a^4*b^8 + 6*a^2*b^10 + b^12)*cos(2*c)^2 + (4*a^10*b^2 + 16*a^8*b^4 + 24*a^6*b^6 + 17*a^4*b^8 + 6*a^2*b^10 + b^12)*sin(2*c)^2)*d*x^2*sin(2*d*x^2)^2 + (a^12 + 2*a^10*b^2 + a^8*b^4)*d*x^2*sin(2*d*x^2 + 2*c)^2 - 2*((a^8*b^4 + 4*a^6*b^6 + 6*a^4*b^8 + 4*a^2*b^10 + b^12)*cos(2*c) - 2*(a^11*b + 5*a^9*b^3 + 10*a^7*b^5 + 10*a^5*b^7 + 5*a^3*b^9 + a*b^11)*sin(2*c))*d*x^2*cos(2*d*x^2) + 2*(2*(a^11*b + 5*a^9*b^3 + 10*a^7*b^5 + 10*a^5*b^7 + 5*a^3*b^9 + a*b^11)*cos(2*c) + (a^8*b^4 + 4*a^6*b^6 + 6*a^4*b^8 + 4*a^2*b^10 + b^12)*sin(2*c))*d*x^2*sin(2*d*x^2) + (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*x^2 - 2*(((a^8*b^4 + 2*a^6*b^6 + a^4*b^8)*cos(2*c) - 2*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*sin(2*c))*d*x^2*cos(2*d*x^2) - (2*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*cos(2*c) + (a^8*b^4 + 2*a^6*b^6 + a^4*b^8)*sin(2*c))*d*x^2*sin(2*d*x^2) - (a^12 + 4*a^10*b^2 + 6*a^8*b^4 + 4*a^6*b^6 + a^4*b^8)*d*x^2)*cos(2*d*x^2 + 2*c) - 2*((2*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*cos(2*c) + (a^8*b^4 + 2*a^6*b^6 + a^4*b^8)*sin(2*c))*d*x^2*cos(2*d*x^2) + ((a^8*b^4 + 2*a^6*b^6 + a^4*b^8)*cos(2*c) - 2*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*sin(2*c))*d*x^2*sin(2*d*x^2))*sin(2*d*x^2 + 2*c))","F",0
24,-1,0,0,0.000000," ","integrate(1/x^2/(a+b*tan(d*x^2+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
25,1,937,0,0.751570," ","integrate(x^3*(a+b*tan(c+d*x^(1/2))),x, algorithm=""maxima"")","\frac{105 \, {\left(d \sqrt{x} + c\right)}^{8} a + 105 i \, {\left(d \sqrt{x} + c\right)}^{8} b - 840 \, {\left(d \sqrt{x} + c\right)}^{7} a c - 840 i \, {\left(d \sqrt{x} + c\right)}^{7} b c + 2940 \, {\left(d \sqrt{x} + c\right)}^{6} a c^{2} + 2940 i \, {\left(d \sqrt{x} + c\right)}^{6} b c^{2} - 5880 \, {\left(d \sqrt{x} + c\right)}^{5} a c^{3} - 5880 i \, {\left(d \sqrt{x} + c\right)}^{5} b c^{3} + 7350 \, {\left(d \sqrt{x} + c\right)}^{4} a c^{4} + 7350 i \, {\left(d \sqrt{x} + c\right)}^{4} b c^{4} - 5880 \, {\left(d \sqrt{x} + c\right)}^{3} a c^{5} - 5880 i \, {\left(d \sqrt{x} + c\right)}^{3} b c^{5} + 2940 \, {\left(d \sqrt{x} + c\right)}^{2} a c^{6} + 2940 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{6} - 840 \, {\left(d \sqrt{x} + c\right)} a c^{7} - 840 \, b c^{7} \log\left(\sec\left(d \sqrt{x} + c\right)\right) - {\left(7680 i \, {\left(d \sqrt{x} + c\right)}^{7} b - 31360 i \, {\left(d \sqrt{x} + c\right)}^{6} b c + 56448 i \, {\left(d \sqrt{x} + c\right)}^{5} b c^{2} - 58800 i \, {\left(d \sqrt{x} + c\right)}^{4} b c^{3} + 39200 i \, {\left(d \sqrt{x} + c\right)}^{3} b c^{4} - 17640 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{5} + 5880 i \, {\left(d \sqrt{x} + c\right)} b c^{6}\right)} \arctan\left(\sin\left(2 \, d \sqrt{x} + 2 \, c\right), \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 1\right) - {\left(-26880 i \, {\left(d \sqrt{x} + c\right)}^{6} b + 94080 i \, {\left(d \sqrt{x} + c\right)}^{5} b c - 141120 i \, {\left(d \sqrt{x} + c\right)}^{4} b c^{2} + 117600 i \, {\left(d \sqrt{x} + c\right)}^{3} b c^{3} - 58800 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{4} + 17640 i \, {\left(d \sqrt{x} + c\right)} b c^{5} - 2940 i \, b c^{6}\right)} {\rm Li}_2\left(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}\right) - 4 \, {\left(960 \, {\left(d \sqrt{x} + c\right)}^{7} b - 3920 \, {\left(d \sqrt{x} + c\right)}^{6} b c + 7056 \, {\left(d \sqrt{x} + c\right)}^{5} b c^{2} - 7350 \, {\left(d \sqrt{x} + c\right)}^{4} b c^{3} + 4900 \, {\left(d \sqrt{x} + c\right)}^{3} b c^{4} - 2205 \, {\left(d \sqrt{x} + c\right)}^{2} b c^{5} + 735 \, {\left(d \sqrt{x} + c\right)} b c^{6}\right)} \log\left(\cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 1\right) - 302400 i \, b {\rm Li}_{8}(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}) - 50400 \, {\left(12 \, {\left(d \sqrt{x} + c\right)} b - 7 \, b c\right)} {\rm Li}_{7}(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}) - {\left(-604800 i \, {\left(d \sqrt{x} + c\right)}^{2} b + 705600 i \, {\left(d \sqrt{x} + c\right)} b c - 211680 i \, b c^{2}\right)} {\rm Li}_{6}(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}) + 2520 \, {\left(160 \, {\left(d \sqrt{x} + c\right)}^{3} b - 280 \, {\left(d \sqrt{x} + c\right)}^{2} b c + 168 \, {\left(d \sqrt{x} + c\right)} b c^{2} - 35 \, b c^{3}\right)} {\rm Li}_{5}(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}) - {\left(201600 i \, {\left(d \sqrt{x} + c\right)}^{4} b - 470400 i \, {\left(d \sqrt{x} + c\right)}^{3} b c + 423360 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{2} - 176400 i \, {\left(d \sqrt{x} + c\right)} b c^{3} + 29400 i \, b c^{4}\right)} {\rm Li}_{4}(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}) - 420 \, {\left(192 \, {\left(d \sqrt{x} + c\right)}^{5} b - 560 \, {\left(d \sqrt{x} + c\right)}^{4} b c + 672 \, {\left(d \sqrt{x} + c\right)}^{3} b c^{2} - 420 \, {\left(d \sqrt{x} + c\right)}^{2} b c^{3} + 140 \, {\left(d \sqrt{x} + c\right)} b c^{4} - 21 \, b c^{5}\right)} {\rm Li}_{3}(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)})}{420 \, d^{8}}"," ",0,"1/420*(105*(d*sqrt(x) + c)^8*a + 105*I*(d*sqrt(x) + c)^8*b - 840*(d*sqrt(x) + c)^7*a*c - 840*I*(d*sqrt(x) + c)^7*b*c + 2940*(d*sqrt(x) + c)^6*a*c^2 + 2940*I*(d*sqrt(x) + c)^6*b*c^2 - 5880*(d*sqrt(x) + c)^5*a*c^3 - 5880*I*(d*sqrt(x) + c)^5*b*c^3 + 7350*(d*sqrt(x) + c)^4*a*c^4 + 7350*I*(d*sqrt(x) + c)^4*b*c^4 - 5880*(d*sqrt(x) + c)^3*a*c^5 - 5880*I*(d*sqrt(x) + c)^3*b*c^5 + 2940*(d*sqrt(x) + c)^2*a*c^6 + 2940*I*(d*sqrt(x) + c)^2*b*c^6 - 840*(d*sqrt(x) + c)*a*c^7 - 840*b*c^7*log(sec(d*sqrt(x) + c)) - (7680*I*(d*sqrt(x) + c)^7*b - 31360*I*(d*sqrt(x) + c)^6*b*c + 56448*I*(d*sqrt(x) + c)^5*b*c^2 - 58800*I*(d*sqrt(x) + c)^4*b*c^3 + 39200*I*(d*sqrt(x) + c)^3*b*c^4 - 17640*I*(d*sqrt(x) + c)^2*b*c^5 + 5880*I*(d*sqrt(x) + c)*b*c^6)*arctan2(sin(2*d*sqrt(x) + 2*c), cos(2*d*sqrt(x) + 2*c) + 1) - (-26880*I*(d*sqrt(x) + c)^6*b + 94080*I*(d*sqrt(x) + c)^5*b*c - 141120*I*(d*sqrt(x) + c)^4*b*c^2 + 117600*I*(d*sqrt(x) + c)^3*b*c^3 - 58800*I*(d*sqrt(x) + c)^2*b*c^4 + 17640*I*(d*sqrt(x) + c)*b*c^5 - 2940*I*b*c^6)*dilog(-e^(2*I*d*sqrt(x) + 2*I*c)) - 4*(960*(d*sqrt(x) + c)^7*b - 3920*(d*sqrt(x) + c)^6*b*c + 7056*(d*sqrt(x) + c)^5*b*c^2 - 7350*(d*sqrt(x) + c)^4*b*c^3 + 4900*(d*sqrt(x) + c)^3*b*c^4 - 2205*(d*sqrt(x) + c)^2*b*c^5 + 735*(d*sqrt(x) + c)*b*c^6)*log(cos(2*d*sqrt(x) + 2*c)^2 + sin(2*d*sqrt(x) + 2*c)^2 + 2*cos(2*d*sqrt(x) + 2*c) + 1) - 302400*I*b*polylog(8, -e^(2*I*d*sqrt(x) + 2*I*c)) - 50400*(12*(d*sqrt(x) + c)*b - 7*b*c)*polylog(7, -e^(2*I*d*sqrt(x) + 2*I*c)) - (-604800*I*(d*sqrt(x) + c)^2*b + 705600*I*(d*sqrt(x) + c)*b*c - 211680*I*b*c^2)*polylog(6, -e^(2*I*d*sqrt(x) + 2*I*c)) + 2520*(160*(d*sqrt(x) + c)^3*b - 280*(d*sqrt(x) + c)^2*b*c + 168*(d*sqrt(x) + c)*b*c^2 - 35*b*c^3)*polylog(5, -e^(2*I*d*sqrt(x) + 2*I*c)) - (201600*I*(d*sqrt(x) + c)^4*b - 470400*I*(d*sqrt(x) + c)^3*b*c + 423360*I*(d*sqrt(x) + c)^2*b*c^2 - 176400*I*(d*sqrt(x) + c)*b*c^3 + 29400*I*b*c^4)*polylog(4, -e^(2*I*d*sqrt(x) + 2*I*c)) - 420*(192*(d*sqrt(x) + c)^5*b - 560*(d*sqrt(x) + c)^4*b*c + 672*(d*sqrt(x) + c)^3*b*c^2 - 420*(d*sqrt(x) + c)^2*b*c^3 + 140*(d*sqrt(x) + c)*b*c^4 - 21*b*c^5)*polylog(3, -e^(2*I*d*sqrt(x) + 2*I*c)))/d^8","B",0
26,1,618,0,1.010386," ","integrate(x^2*(a+b*tan(c+d*x^(1/2))),x, algorithm=""maxima"")","\frac{5 \, {\left(d \sqrt{x} + c\right)}^{6} a + 5 i \, {\left(d \sqrt{x} + c\right)}^{6} b - 30 \, {\left(d \sqrt{x} + c\right)}^{5} a c - 30 i \, {\left(d \sqrt{x} + c\right)}^{5} b c + 75 \, {\left(d \sqrt{x} + c\right)}^{4} a c^{2} + 75 i \, {\left(d \sqrt{x} + c\right)}^{4} b c^{2} - 100 \, {\left(d \sqrt{x} + c\right)}^{3} a c^{3} - 100 i \, {\left(d \sqrt{x} + c\right)}^{3} b c^{3} + 75 \, {\left(d \sqrt{x} + c\right)}^{2} a c^{4} + 75 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{4} - 30 \, {\left(d \sqrt{x} + c\right)} a c^{5} - 30 \, b c^{5} \log\left(\sec\left(d \sqrt{x} + c\right)\right) - {\left(96 i \, {\left(d \sqrt{x} + c\right)}^{5} b - 300 i \, {\left(d \sqrt{x} + c\right)}^{4} b c + 400 i \, {\left(d \sqrt{x} + c\right)}^{3} b c^{2} - 300 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{3} + 150 i \, {\left(d \sqrt{x} + c\right)} b c^{4}\right)} \arctan\left(\sin\left(2 \, d \sqrt{x} + 2 \, c\right), \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 1\right) - {\left(-240 i \, {\left(d \sqrt{x} + c\right)}^{4} b + 600 i \, {\left(d \sqrt{x} + c\right)}^{3} b c - 600 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{2} + 300 i \, {\left(d \sqrt{x} + c\right)} b c^{3} - 75 i \, b c^{4}\right)} {\rm Li}_2\left(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}\right) - {\left(48 \, {\left(d \sqrt{x} + c\right)}^{5} b - 150 \, {\left(d \sqrt{x} + c\right)}^{4} b c + 200 \, {\left(d \sqrt{x} + c\right)}^{3} b c^{2} - 150 \, {\left(d \sqrt{x} + c\right)}^{2} b c^{3} + 75 \, {\left(d \sqrt{x} + c\right)} b c^{4}\right)} \log\left(\cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 1\right) + 360 i \, b {\rm Li}_{6}(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}) + 90 \, {\left(8 \, {\left(d \sqrt{x} + c\right)} b - 5 \, b c\right)} {\rm Li}_{5}(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}) - {\left(720 i \, {\left(d \sqrt{x} + c\right)}^{2} b - 900 i \, {\left(d \sqrt{x} + c\right)} b c + 300 i \, b c^{2}\right)} {\rm Li}_{4}(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}) - 30 \, {\left(16 \, {\left(d \sqrt{x} + c\right)}^{3} b - 30 \, {\left(d \sqrt{x} + c\right)}^{2} b c + 20 \, {\left(d \sqrt{x} + c\right)} b c^{2} - 5 \, b c^{3}\right)} {\rm Li}_{3}(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)})}{15 \, d^{6}}"," ",0,"1/15*(5*(d*sqrt(x) + c)^6*a + 5*I*(d*sqrt(x) + c)^6*b - 30*(d*sqrt(x) + c)^5*a*c - 30*I*(d*sqrt(x) + c)^5*b*c + 75*(d*sqrt(x) + c)^4*a*c^2 + 75*I*(d*sqrt(x) + c)^4*b*c^2 - 100*(d*sqrt(x) + c)^3*a*c^3 - 100*I*(d*sqrt(x) + c)^3*b*c^3 + 75*(d*sqrt(x) + c)^2*a*c^4 + 75*I*(d*sqrt(x) + c)^2*b*c^4 - 30*(d*sqrt(x) + c)*a*c^5 - 30*b*c^5*log(sec(d*sqrt(x) + c)) - (96*I*(d*sqrt(x) + c)^5*b - 300*I*(d*sqrt(x) + c)^4*b*c + 400*I*(d*sqrt(x) + c)^3*b*c^2 - 300*I*(d*sqrt(x) + c)^2*b*c^3 + 150*I*(d*sqrt(x) + c)*b*c^4)*arctan2(sin(2*d*sqrt(x) + 2*c), cos(2*d*sqrt(x) + 2*c) + 1) - (-240*I*(d*sqrt(x) + c)^4*b + 600*I*(d*sqrt(x) + c)^3*b*c - 600*I*(d*sqrt(x) + c)^2*b*c^2 + 300*I*(d*sqrt(x) + c)*b*c^3 - 75*I*b*c^4)*dilog(-e^(2*I*d*sqrt(x) + 2*I*c)) - (48*(d*sqrt(x) + c)^5*b - 150*(d*sqrt(x) + c)^4*b*c + 200*(d*sqrt(x) + c)^3*b*c^2 - 150*(d*sqrt(x) + c)^2*b*c^3 + 75*(d*sqrt(x) + c)*b*c^4)*log(cos(2*d*sqrt(x) + 2*c)^2 + sin(2*d*sqrt(x) + 2*c)^2 + 2*cos(2*d*sqrt(x) + 2*c) + 1) + 360*I*b*polylog(6, -e^(2*I*d*sqrt(x) + 2*I*c)) + 90*(8*(d*sqrt(x) + c)*b - 5*b*c)*polylog(5, -e^(2*I*d*sqrt(x) + 2*I*c)) - (720*I*(d*sqrt(x) + c)^2*b - 900*I*(d*sqrt(x) + c)*b*c + 300*I*b*c^2)*polylog(4, -e^(2*I*d*sqrt(x) + 2*I*c)) - 30*(16*(d*sqrt(x) + c)^3*b - 30*(d*sqrt(x) + c)^2*b*c + 20*(d*sqrt(x) + c)*b*c^2 - 5*b*c^3)*polylog(3, -e^(2*I*d*sqrt(x) + 2*I*c)))/d^6","B",0
27,1,359,0,0.563253," ","integrate(x*(a+b*tan(c+d*x^(1/2))),x, algorithm=""maxima"")","\frac{3 \, {\left(d \sqrt{x} + c\right)}^{4} a + 3 i \, {\left(d \sqrt{x} + c\right)}^{4} b - 12 \, {\left(d \sqrt{x} + c\right)}^{3} a c - 12 i \, {\left(d \sqrt{x} + c\right)}^{3} b c + 18 \, {\left(d \sqrt{x} + c\right)}^{2} a c^{2} + 18 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{2} - 12 \, {\left(d \sqrt{x} + c\right)} a c^{3} - 12 \, b c^{3} \log\left(\sec\left(d \sqrt{x} + c\right)\right) - {\left(16 i \, {\left(d \sqrt{x} + c\right)}^{3} b - 36 i \, {\left(d \sqrt{x} + c\right)}^{2} b c + 36 i \, {\left(d \sqrt{x} + c\right)} b c^{2}\right)} \arctan\left(\sin\left(2 \, d \sqrt{x} + 2 \, c\right), \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 1\right) - {\left(-24 i \, {\left(d \sqrt{x} + c\right)}^{2} b + 36 i \, {\left(d \sqrt{x} + c\right)} b c - 18 i \, b c^{2}\right)} {\rm Li}_2\left(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}\right) - 2 \, {\left(4 \, {\left(d \sqrt{x} + c\right)}^{3} b - 9 \, {\left(d \sqrt{x} + c\right)}^{2} b c + 9 \, {\left(d \sqrt{x} + c\right)} b c^{2}\right)} \log\left(\cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 1\right) - 12 i \, b {\rm Li}_{4}(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}) - 6 \, {\left(4 \, {\left(d \sqrt{x} + c\right)} b - 3 \, b c\right)} {\rm Li}_{3}(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)})}{6 \, d^{4}}"," ",0,"1/6*(3*(d*sqrt(x) + c)^4*a + 3*I*(d*sqrt(x) + c)^4*b - 12*(d*sqrt(x) + c)^3*a*c - 12*I*(d*sqrt(x) + c)^3*b*c + 18*(d*sqrt(x) + c)^2*a*c^2 + 18*I*(d*sqrt(x) + c)^2*b*c^2 - 12*(d*sqrt(x) + c)*a*c^3 - 12*b*c^3*log(sec(d*sqrt(x) + c)) - (16*I*(d*sqrt(x) + c)^3*b - 36*I*(d*sqrt(x) + c)^2*b*c + 36*I*(d*sqrt(x) + c)*b*c^2)*arctan2(sin(2*d*sqrt(x) + 2*c), cos(2*d*sqrt(x) + 2*c) + 1) - (-24*I*(d*sqrt(x) + c)^2*b + 36*I*(d*sqrt(x) + c)*b*c - 18*I*b*c^2)*dilog(-e^(2*I*d*sqrt(x) + 2*I*c)) - 2*(4*(d*sqrt(x) + c)^3*b - 9*(d*sqrt(x) + c)^2*b*c + 9*(d*sqrt(x) + c)*b*c^2)*log(cos(2*d*sqrt(x) + 2*c)^2 + sin(2*d*sqrt(x) + 2*c)^2 + 2*cos(2*d*sqrt(x) + 2*c) + 1) - 12*I*b*polylog(4, -e^(2*I*d*sqrt(x) + 2*I*c)) - 6*(4*(d*sqrt(x) + c)*b - 3*b*c)*polylog(3, -e^(2*I*d*sqrt(x) + 2*I*c)))/d^4","B",0
28,0,0,0,0.000000," ","integrate(a+b*tan(c+d*x^(1/2)),x, algorithm=""maxima"")","a x + 2 \, b \int \frac{\sin\left(2 \, d \sqrt{x} + 2 \, c\right)}{\cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 1}\,{d x}"," ",0,"a*x + 2*b*integrate(sin(2*d*sqrt(x) + 2*c)/(cos(2*d*sqrt(x) + 2*c)^2 + sin(2*d*sqrt(x) + 2*c)^2 + 2*cos(2*d*sqrt(x) + 2*c) + 1), x)","F",0
29,0,0,0,0.000000," ","integrate((a+b*tan(c+d*x^(1/2)))/x,x, algorithm=""maxima"")","2 \, b \int \frac{\sin\left(2 \, d \sqrt{x} + 2 \, c\right)}{{\left(\cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 1\right)} x}\,{d x} + a \log\left(x\right)"," ",0,"2*b*integrate(sin(2*d*sqrt(x) + 2*c)/((cos(2*d*sqrt(x) + 2*c)^2 + sin(2*d*sqrt(x) + 2*c)^2 + 2*cos(2*d*sqrt(x) + 2*c) + 1)*x), x) + a*log(x)","F",0
30,0,0,0,0.000000," ","integrate((a+b*tan(c+d*x^(1/2)))/x^2,x, algorithm=""maxima"")","\frac{2 \, b x \int \frac{\sin\left(2 \, d \sqrt{x} + 2 \, c\right)}{{\left(\cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 1\right)} x^{2}}\,{d x} - a}{x}"," ",0,"(2*b*x*integrate(sin(2*d*sqrt(x) + 2*c)/((cos(2*d*sqrt(x) + 2*c)^2 + sin(2*d*sqrt(x) + 2*c)^2 + 2*cos(2*d*sqrt(x) + 2*c) + 1)*x^2), x) - a)/x","F",0
31,1,2400,0,1.266112," ","integrate(x^2*(a+b*tan(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","\frac{{\left(d \sqrt{x} + c\right)}^{6} a^{2} - 6 \, {\left(d \sqrt{x} + c\right)}^{5} a^{2} c + 15 \, {\left(d \sqrt{x} + c\right)}^{4} a^{2} c^{2} - 20 \, {\left(d \sqrt{x} + c\right)}^{3} a^{2} c^{3} + 15 \, {\left(d \sqrt{x} + c\right)}^{2} a^{2} c^{4} - 6 \, {\left(d \sqrt{x} + c\right)} a^{2} c^{5} - 12 \, a b c^{5} \log\left(\sec\left(d \sqrt{x} + c\right)\right) - \frac{6 \, {\left(30 i \, {\left(d \sqrt{x} + c\right)} b^{2} c^{5} - 5 \, {\left(2 \, a b + i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{6} + 30 \, {\left(2 \, a b + i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{5} c - 75 \, {\left(2 \, a b + i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} c^{2} + 100 \, {\left(2 \, a b + i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} c^{3} - 75 \, {\left(2 \, a b + i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} c^{4} + 60 \, b^{2} c^{5} + {\left(192 \, {\left(d \sqrt{x} + c\right)}^{5} a b - 150 \, b^{2} c^{4} - 300 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + 800 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{3} - 300 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 300 \, {\left(a b c^{4} + 2 \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)} + 2 \, {\left(96 \, {\left(d \sqrt{x} + c\right)}^{5} a b - 75 \, b^{2} c^{4} - 150 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + 400 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{3} - 150 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 150 \, {\left(a b c^{4} + 2 \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(192 i \, {\left(d \sqrt{x} + c\right)}^{5} a b - 150 i \, b^{2} c^{4} + {\left(-600 i \, a b c - 300 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left(800 i \, a b c^{2} + 800 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(-600 i \, a b c^{3} - 900 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(300 i \, a b c^{4} + 600 i \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \arctan\left(\sin\left(2 \, d \sqrt{x} + 2 \, c\right), \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 1\right) - 5 \, {\left({\left(2 \, a b + i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{6} - 6 \, {\left(2 \, b^{2} + {\left(2 \, a b + i \, b^{2}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{5} + 15 \, {\left(4 \, b^{2} c + {\left(2 \, a b + i \, b^{2}\right)} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} - 20 \, {\left(6 \, b^{2} c^{2} + {\left(2 \, a b + i \, b^{2}\right)} c^{3}\right)} {\left(d \sqrt{x} + c\right)}^{3} + 15 \, {\left(8 \, b^{2} c^{3} + {\left(2 \, a b + i \, b^{2}\right)} c^{4}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 6 \, {\left(-i \, b^{2} c^{5} - 10 \, b^{2} c^{4}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(480 \, {\left(d \sqrt{x} + c\right)}^{4} a b + 150 \, a b c^{4} + 300 \, b^{2} c^{3} - 600 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + 1200 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{2} - 300 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)} + 30 \, {\left(16 \, {\left(d \sqrt{x} + c\right)}^{4} a b + 5 \, a b c^{4} + 10 \, b^{2} c^{3} - 20 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + 40 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{2} - 10 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(-480 i \, {\left(d \sqrt{x} + c\right)}^{4} a b - 150 i \, a b c^{4} - 300 i \, b^{2} c^{3} + {\left(1200 i \, a b c + 600 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(-1200 i \, a b c^{2} - 1200 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(600 i \, a b c^{3} + 900 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_2\left(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}\right) + {\left(-96 i \, {\left(d \sqrt{x} + c\right)}^{5} a b + 75 i \, b^{2} c^{4} + {\left(300 i \, a b c + 150 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left(-400 i \, a b c^{2} - 400 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(300 i \, a b c^{3} + 450 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(-150 i \, a b c^{4} - 300 i \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)} + {\left(-96 i \, {\left(d \sqrt{x} + c\right)}^{5} a b + 75 i \, b^{2} c^{4} + {\left(300 i \, a b c + 150 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left(-400 i \, a b c^{2} - 400 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(300 i \, a b c^{3} + 450 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(-150 i \, a b c^{4} - 300 i \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(96 \, {\left(d \sqrt{x} + c\right)}^{5} a b - 75 \, b^{2} c^{4} - 150 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + 400 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)}^{3} - 150 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 150 \, {\left(a b c^{4} + 2 \, b^{2} c^{3}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \log\left(\cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 1\right) - 720 \, {\left(a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + i \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + a b\right)} {\rm Li}_{6}(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}) + {\left(1440 i \, {\left(d \sqrt{x} + c\right)} a b - 900 i \, a b c - 450 i \, b^{2} + {\left(1440 i \, {\left(d \sqrt{x} + c\right)} a b - 900 i \, a b c - 450 i \, b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 90 \, {\left(16 \, {\left(d \sqrt{x} + c\right)} a b - 10 \, a b c - 5 \, b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{5}(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}) + {\left(1440 \, {\left(d \sqrt{x} + c\right)}^{2} a b + 600 \, a b c^{2} + 600 \, b^{2} c - 900 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)} + 60 \, {\left(24 \, {\left(d \sqrt{x} + c\right)}^{2} a b + 10 \, a b c^{2} + 10 \, b^{2} c - 15 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(1440 i \, {\left(d \sqrt{x} + c\right)}^{2} a b + 600 i \, a b c^{2} + 600 i \, b^{2} c + {\left(-1800 i \, a b c - 900 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{4}(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}) + {\left(-960 i \, {\left(d \sqrt{x} + c\right)}^{3} a b + 300 i \, a b c^{3} + 450 i \, b^{2} c^{2} + {\left(1800 i \, a b c + 900 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(-1200 i \, a b c^{2} - 1200 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)} + {\left(-960 i \, {\left(d \sqrt{x} + c\right)}^{3} a b + 300 i \, a b c^{3} + 450 i \, b^{2} c^{2} + {\left(1800 i \, a b c + 900 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(-1200 i \, a b c^{2} - 1200 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 30 \, {\left(32 \, {\left(d \sqrt{x} + c\right)}^{3} a b - 10 \, a b c^{3} - 15 \, b^{2} c^{2} - 30 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 40 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{3}(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}) + {\left({\left(-10 i \, a b + 5 \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{6} + {\left(60 i \, b^{2} + {\left(60 i \, a b - 30 \, b^{2}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{5} + {\left(-300 i \, b^{2} c + {\left(-150 i \, a b + 75 \, b^{2}\right)} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left(600 i \, b^{2} c^{2} + {\left(200 i \, a b - 100 \, b^{2}\right)} c^{3}\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(-600 i \, b^{2} c^{3} + {\left(-150 i \, a b + 75 \, b^{2}\right)} c^{4}\right)} {\left(d \sqrt{x} + c\right)}^{2} - {\left(30 \, b^{2} c^{5} - 300 i \, b^{2} c^{4}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)}}{-30 i \, \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 30 \, \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - 30 i}}{3 \, d^{6}}"," ",0,"1/3*((d*sqrt(x) + c)^6*a^2 - 6*(d*sqrt(x) + c)^5*a^2*c + 15*(d*sqrt(x) + c)^4*a^2*c^2 - 20*(d*sqrt(x) + c)^3*a^2*c^3 + 15*(d*sqrt(x) + c)^2*a^2*c^4 - 6*(d*sqrt(x) + c)*a^2*c^5 - 12*a*b*c^5*log(sec(d*sqrt(x) + c)) - 6*(30*I*(d*sqrt(x) + c)*b^2*c^5 - 5*(2*a*b + I*b^2)*(d*sqrt(x) + c)^6 + 30*(2*a*b + I*b^2)*(d*sqrt(x) + c)^5*c - 75*(2*a*b + I*b^2)*(d*sqrt(x) + c)^4*c^2 + 100*(2*a*b + I*b^2)*(d*sqrt(x) + c)^3*c^3 - 75*(2*a*b + I*b^2)*(d*sqrt(x) + c)^2*c^4 + 60*b^2*c^5 + (192*(d*sqrt(x) + c)^5*a*b - 150*b^2*c^4 - 300*(2*a*b*c + b^2)*(d*sqrt(x) + c)^4 + 800*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c)^3 - 300*(2*a*b*c^3 + 3*b^2*c^2)*(d*sqrt(x) + c)^2 + 300*(a*b*c^4 + 2*b^2*c^3)*(d*sqrt(x) + c) + 2*(96*(d*sqrt(x) + c)^5*a*b - 75*b^2*c^4 - 150*(2*a*b*c + b^2)*(d*sqrt(x) + c)^4 + 400*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c)^3 - 150*(2*a*b*c^3 + 3*b^2*c^2)*(d*sqrt(x) + c)^2 + 150*(a*b*c^4 + 2*b^2*c^3)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) + (192*I*(d*sqrt(x) + c)^5*a*b - 150*I*b^2*c^4 + (-600*I*a*b*c - 300*I*b^2)*(d*sqrt(x) + c)^4 + (800*I*a*b*c^2 + 800*I*b^2*c)*(d*sqrt(x) + c)^3 + (-600*I*a*b*c^3 - 900*I*b^2*c^2)*(d*sqrt(x) + c)^2 + (300*I*a*b*c^4 + 600*I*b^2*c^3)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*arctan2(sin(2*d*sqrt(x) + 2*c), cos(2*d*sqrt(x) + 2*c) + 1) - 5*((2*a*b + I*b^2)*(d*sqrt(x) + c)^6 - 6*(2*b^2 + (2*a*b + I*b^2)*c)*(d*sqrt(x) + c)^5 + 15*(4*b^2*c + (2*a*b + I*b^2)*c^2)*(d*sqrt(x) + c)^4 - 20*(6*b^2*c^2 + (2*a*b + I*b^2)*c^3)*(d*sqrt(x) + c)^3 + 15*(8*b^2*c^3 + (2*a*b + I*b^2)*c^4)*(d*sqrt(x) + c)^2 + 6*(-I*b^2*c^5 - 10*b^2*c^4)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) - (480*(d*sqrt(x) + c)^4*a*b + 150*a*b*c^4 + 300*b^2*c^3 - 600*(2*a*b*c + b^2)*(d*sqrt(x) + c)^3 + 1200*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c)^2 - 300*(2*a*b*c^3 + 3*b^2*c^2)*(d*sqrt(x) + c) + 30*(16*(d*sqrt(x) + c)^4*a*b + 5*a*b*c^4 + 10*b^2*c^3 - 20*(2*a*b*c + b^2)*(d*sqrt(x) + c)^3 + 40*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c)^2 - 10*(2*a*b*c^3 + 3*b^2*c^2)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) - (-480*I*(d*sqrt(x) + c)^4*a*b - 150*I*a*b*c^4 - 300*I*b^2*c^3 + (1200*I*a*b*c + 600*I*b^2)*(d*sqrt(x) + c)^3 + (-1200*I*a*b*c^2 - 1200*I*b^2*c)*(d*sqrt(x) + c)^2 + (600*I*a*b*c^3 + 900*I*b^2*c^2)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*dilog(-e^(2*I*d*sqrt(x) + 2*I*c)) + (-96*I*(d*sqrt(x) + c)^5*a*b + 75*I*b^2*c^4 + (300*I*a*b*c + 150*I*b^2)*(d*sqrt(x) + c)^4 + (-400*I*a*b*c^2 - 400*I*b^2*c)*(d*sqrt(x) + c)^3 + (300*I*a*b*c^3 + 450*I*b^2*c^2)*(d*sqrt(x) + c)^2 + (-150*I*a*b*c^4 - 300*I*b^2*c^3)*(d*sqrt(x) + c) + (-96*I*(d*sqrt(x) + c)^5*a*b + 75*I*b^2*c^4 + (300*I*a*b*c + 150*I*b^2)*(d*sqrt(x) + c)^4 + (-400*I*a*b*c^2 - 400*I*b^2*c)*(d*sqrt(x) + c)^3 + (300*I*a*b*c^3 + 450*I*b^2*c^2)*(d*sqrt(x) + c)^2 + (-150*I*a*b*c^4 - 300*I*b^2*c^3)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) + (96*(d*sqrt(x) + c)^5*a*b - 75*b^2*c^4 - 150*(2*a*b*c + b^2)*(d*sqrt(x) + c)^4 + 400*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c)^3 - 150*(2*a*b*c^3 + 3*b^2*c^2)*(d*sqrt(x) + c)^2 + 150*(a*b*c^4 + 2*b^2*c^3)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*log(cos(2*d*sqrt(x) + 2*c)^2 + sin(2*d*sqrt(x) + 2*c)^2 + 2*cos(2*d*sqrt(x) + 2*c) + 1) - 720*(a*b*cos(2*d*sqrt(x) + 2*c) + I*a*b*sin(2*d*sqrt(x) + 2*c) + a*b)*polylog(6, -e^(2*I*d*sqrt(x) + 2*I*c)) + (1440*I*(d*sqrt(x) + c)*a*b - 900*I*a*b*c - 450*I*b^2 + (1440*I*(d*sqrt(x) + c)*a*b - 900*I*a*b*c - 450*I*b^2)*cos(2*d*sqrt(x) + 2*c) - 90*(16*(d*sqrt(x) + c)*a*b - 10*a*b*c - 5*b^2)*sin(2*d*sqrt(x) + 2*c))*polylog(5, -e^(2*I*d*sqrt(x) + 2*I*c)) + (1440*(d*sqrt(x) + c)^2*a*b + 600*a*b*c^2 + 600*b^2*c - 900*(2*a*b*c + b^2)*(d*sqrt(x) + c) + 60*(24*(d*sqrt(x) + c)^2*a*b + 10*a*b*c^2 + 10*b^2*c - 15*(2*a*b*c + b^2)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) + (1440*I*(d*sqrt(x) + c)^2*a*b + 600*I*a*b*c^2 + 600*I*b^2*c + (-1800*I*a*b*c - 900*I*b^2)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*polylog(4, -e^(2*I*d*sqrt(x) + 2*I*c)) + (-960*I*(d*sqrt(x) + c)^3*a*b + 300*I*a*b*c^3 + 450*I*b^2*c^2 + (1800*I*a*b*c + 900*I*b^2)*(d*sqrt(x) + c)^2 + (-1200*I*a*b*c^2 - 1200*I*b^2*c)*(d*sqrt(x) + c) + (-960*I*(d*sqrt(x) + c)^3*a*b + 300*I*a*b*c^3 + 450*I*b^2*c^2 + (1800*I*a*b*c + 900*I*b^2)*(d*sqrt(x) + c)^2 + (-1200*I*a*b*c^2 - 1200*I*b^2*c)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) + 30*(32*(d*sqrt(x) + c)^3*a*b - 10*a*b*c^3 - 15*b^2*c^2 - 30*(2*a*b*c + b^2)*(d*sqrt(x) + c)^2 + 40*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*polylog(3, -e^(2*I*d*sqrt(x) + 2*I*c)) + ((-10*I*a*b + 5*b^2)*(d*sqrt(x) + c)^6 + (60*I*b^2 + (60*I*a*b - 30*b^2)*c)*(d*sqrt(x) + c)^5 + (-300*I*b^2*c + (-150*I*a*b + 75*b^2)*c^2)*(d*sqrt(x) + c)^4 + (600*I*b^2*c^2 + (200*I*a*b - 100*b^2)*c^3)*(d*sqrt(x) + c)^3 + (-600*I*b^2*c^3 + (-150*I*a*b + 75*b^2)*c^4)*(d*sqrt(x) + c)^2 - (30*b^2*c^5 - 300*I*b^2*c^4)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))/(-30*I*cos(2*d*sqrt(x) + 2*c) + 30*sin(2*d*sqrt(x) + 2*c) - 30*I))/d^6","B",0
32,1,1282,0,1.125104," ","integrate(x*(a+b*tan(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","\frac{{\left(d \sqrt{x} + c\right)}^{4} a^{2} - 4 \, {\left(d \sqrt{x} + c\right)}^{3} a^{2} c + 6 \, {\left(d \sqrt{x} + c\right)}^{2} a^{2} c^{2} - 4 \, {\left(d \sqrt{x} + c\right)} a^{2} c^{3} - 8 \, a b c^{3} \log\left(\sec\left(d \sqrt{x} + c\right)\right) - \frac{4 \, {\left(12 i \, {\left(d \sqrt{x} + c\right)} b^{2} c^{3} - 3 \, {\left(2 \, a b + i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + 12 \, {\left(2 \, a b + i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} c - 18 \, {\left(2 \, a b + i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} c^{2} + 24 \, b^{2} c^{3} + {\left(32 \, {\left(d \sqrt{x} + c\right)}^{3} a b - 36 \, b^{2} c^{2} - 36 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 72 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)} + 4 \, {\left(8 \, {\left(d \sqrt{x} + c\right)}^{3} a b - 9 \, b^{2} c^{2} - 9 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 18 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(32 i \, {\left(d \sqrt{x} + c\right)}^{3} a b - 36 i \, b^{2} c^{2} + {\left(-72 i \, a b c - 36 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(72 i \, a b c^{2} + 72 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \arctan\left(\sin\left(2 \, d \sqrt{x} + 2 \, c\right), \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 1\right) - 3 \, {\left({\left(2 \, a b + i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} - 4 \, {\left(2 \, b^{2} + {\left(2 \, a b + i \, b^{2}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{3} + 6 \, {\left(4 \, b^{2} c + {\left(2 \, a b + i \, b^{2}\right)} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 4 \, {\left(-i \, b^{2} c^{3} - 6 \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(48 \, {\left(d \sqrt{x} + c\right)}^{2} a b + 36 \, a b c^{2} + 36 \, b^{2} c - 36 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)} + 12 \, {\left(4 \, {\left(d \sqrt{x} + c\right)}^{2} a b + 3 \, a b c^{2} + 3 \, b^{2} c - 3 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(-48 i \, {\left(d \sqrt{x} + c\right)}^{2} a b - 36 i \, a b c^{2} - 36 i \, b^{2} c + {\left(72 i \, a b c + 36 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_2\left(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}\right) + {\left(-16 i \, {\left(d \sqrt{x} + c\right)}^{3} a b + 18 i \, b^{2} c^{2} + {\left(36 i \, a b c + 18 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(-36 i \, a b c^{2} - 36 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)} + {\left(-16 i \, {\left(d \sqrt{x} + c\right)}^{3} a b + 18 i \, b^{2} c^{2} + {\left(36 i \, a b c + 18 i \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(-36 i \, a b c^{2} - 36 i \, b^{2} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 2 \, {\left(8 \, {\left(d \sqrt{x} + c\right)}^{3} a b - 9 \, b^{2} c^{2} - 9 \, {\left(2 \, a b c + b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 18 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \log\left(\cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 1\right) + 24 \, {\left(a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + i \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + a b\right)} {\rm Li}_{4}(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}) + {\left(-48 i \, {\left(d \sqrt{x} + c\right)} a b + 36 i \, a b c + 18 i \, b^{2} + {\left(-48 i \, {\left(d \sqrt{x} + c\right)} a b + 36 i \, a b c + 18 i \, b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 6 \, {\left(8 \, {\left(d \sqrt{x} + c\right)} a b - 6 \, a b c - 3 \, b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{3}(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}) + {\left({\left(-6 i \, a b + 3 \, b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left(24 i \, b^{2} + {\left(24 i \, a b - 12 \, b^{2}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(-72 i \, b^{2} c + {\left(-36 i \, a b + 18 \, b^{2}\right)} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} - {\left(12 \, b^{2} c^{3} - 72 i \, b^{2} c^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)}}{-12 i \, \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 12 \, \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - 12 i}}{2 \, d^{4}}"," ",0,"1/2*((d*sqrt(x) + c)^4*a^2 - 4*(d*sqrt(x) + c)^3*a^2*c + 6*(d*sqrt(x) + c)^2*a^2*c^2 - 4*(d*sqrt(x) + c)*a^2*c^3 - 8*a*b*c^3*log(sec(d*sqrt(x) + c)) - 4*(12*I*(d*sqrt(x) + c)*b^2*c^3 - 3*(2*a*b + I*b^2)*(d*sqrt(x) + c)^4 + 12*(2*a*b + I*b^2)*(d*sqrt(x) + c)^3*c - 18*(2*a*b + I*b^2)*(d*sqrt(x) + c)^2*c^2 + 24*b^2*c^3 + (32*(d*sqrt(x) + c)^3*a*b - 36*b^2*c^2 - 36*(2*a*b*c + b^2)*(d*sqrt(x) + c)^2 + 72*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c) + 4*(8*(d*sqrt(x) + c)^3*a*b - 9*b^2*c^2 - 9*(2*a*b*c + b^2)*(d*sqrt(x) + c)^2 + 18*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) + (32*I*(d*sqrt(x) + c)^3*a*b - 36*I*b^2*c^2 + (-72*I*a*b*c - 36*I*b^2)*(d*sqrt(x) + c)^2 + (72*I*a*b*c^2 + 72*I*b^2*c)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*arctan2(sin(2*d*sqrt(x) + 2*c), cos(2*d*sqrt(x) + 2*c) + 1) - 3*((2*a*b + I*b^2)*(d*sqrt(x) + c)^4 - 4*(2*b^2 + (2*a*b + I*b^2)*c)*(d*sqrt(x) + c)^3 + 6*(4*b^2*c + (2*a*b + I*b^2)*c^2)*(d*sqrt(x) + c)^2 + 4*(-I*b^2*c^3 - 6*b^2*c^2)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) - (48*(d*sqrt(x) + c)^2*a*b + 36*a*b*c^2 + 36*b^2*c - 36*(2*a*b*c + b^2)*(d*sqrt(x) + c) + 12*(4*(d*sqrt(x) + c)^2*a*b + 3*a*b*c^2 + 3*b^2*c - 3*(2*a*b*c + b^2)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) - (-48*I*(d*sqrt(x) + c)^2*a*b - 36*I*a*b*c^2 - 36*I*b^2*c + (72*I*a*b*c + 36*I*b^2)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*dilog(-e^(2*I*d*sqrt(x) + 2*I*c)) + (-16*I*(d*sqrt(x) + c)^3*a*b + 18*I*b^2*c^2 + (36*I*a*b*c + 18*I*b^2)*(d*sqrt(x) + c)^2 + (-36*I*a*b*c^2 - 36*I*b^2*c)*(d*sqrt(x) + c) + (-16*I*(d*sqrt(x) + c)^3*a*b + 18*I*b^2*c^2 + (36*I*a*b*c + 18*I*b^2)*(d*sqrt(x) + c)^2 + (-36*I*a*b*c^2 - 36*I*b^2*c)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) + 2*(8*(d*sqrt(x) + c)^3*a*b - 9*b^2*c^2 - 9*(2*a*b*c + b^2)*(d*sqrt(x) + c)^2 + 18*(a*b*c^2 + b^2*c)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*log(cos(2*d*sqrt(x) + 2*c)^2 + sin(2*d*sqrt(x) + 2*c)^2 + 2*cos(2*d*sqrt(x) + 2*c) + 1) + 24*(a*b*cos(2*d*sqrt(x) + 2*c) + I*a*b*sin(2*d*sqrt(x) + 2*c) + a*b)*polylog(4, -e^(2*I*d*sqrt(x) + 2*I*c)) + (-48*I*(d*sqrt(x) + c)*a*b + 36*I*a*b*c + 18*I*b^2 + (-48*I*(d*sqrt(x) + c)*a*b + 36*I*a*b*c + 18*I*b^2)*cos(2*d*sqrt(x) + 2*c) + 6*(8*(d*sqrt(x) + c)*a*b - 6*a*b*c - 3*b^2)*sin(2*d*sqrt(x) + 2*c))*polylog(3, -e^(2*I*d*sqrt(x) + 2*I*c)) + ((-6*I*a*b + 3*b^2)*(d*sqrt(x) + c)^4 + (24*I*b^2 + (24*I*a*b - 12*b^2)*c)*(d*sqrt(x) + c)^3 + (-72*I*b^2*c + (-36*I*a*b + 18*b^2)*c^2)*(d*sqrt(x) + c)^2 - (12*b^2*c^3 - 72*I*b^2*c^2)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))/(-12*I*cos(2*d*sqrt(x) + 2*c) + 12*sin(2*d*sqrt(x) + 2*c) - 12*I))/d^4","B",0
33,1,498,0,1.288794," ","integrate((a+b*tan(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","a^{2} x + \frac{4 \, b^{2} d \sqrt{x} + 4 \, {\left(a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + i \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + a b\right)} \arctan\left(\sin\left(2 \, d \sqrt{x} - 2 \, c\right), \cos\left(2 \, d \sqrt{x} - 2 \, c\right) + 1\right) \arctan\left(\sin\left(d \sqrt{x}\right), \cos\left(d \sqrt{x}\right)\right) + {\left(-2 i \, a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 2 \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - 2 i \, a b\right)} \arctan\left(\sin\left(d \sqrt{x}\right), \cos\left(d \sqrt{x}\right)\right) \log\left(\cos\left(2 \, d \sqrt{x} - 2 \, c\right)^{2} + \sin\left(2 \, d \sqrt{x} - 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d \sqrt{x} - 2 \, c\right) + 1\right) - {\left({\left(2 \, a b - i \, b^{2}\right)} d^{2} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(-2 i \, a b - b^{2}\right)} d^{2} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(2 \, a b - i \, b^{2}\right)} d^{2}\right)} x + {\left(2 \, b^{2} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 2 i \, b^{2} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + 2 \, b^{2}\right)} \arctan\left(\sin\left(2 \, d \sqrt{x}\right) + \sin\left(2 \, c\right), \cos\left(2 \, d \sqrt{x}\right) + \cos\left(2 \, c\right)\right) - 2 \, {\left(a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + i \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + a b\right)} {\rm Li}_2\left(-e^{\left(2 i \, d \sqrt{x} - 2 i \, c\right)}\right) + {\left(-i \, b^{2} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + b^{2} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - i \, b^{2}\right)} \log\left(\cos\left(2 \, d \sqrt{x}\right)^{2} + 2 \, \cos\left(2 \, d \sqrt{x}\right) \cos\left(2 \, c\right) + \cos\left(2 \, c\right)^{2} + \sin\left(2 \, d \sqrt{x}\right)^{2} + 2 \, \sin\left(2 \, d \sqrt{x}\right) \sin\left(2 \, c\right) + \sin\left(2 \, c\right)^{2}\right)}{-i \, d^{2} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + d^{2} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - i \, d^{2}}"," ",0,"a^2*x + (4*b^2*d*sqrt(x) + 4*(a*b*cos(2*d*sqrt(x) + 2*c) + I*a*b*sin(2*d*sqrt(x) + 2*c) + a*b)*arctan2(sin(2*d*sqrt(x) - 2*c), cos(2*d*sqrt(x) - 2*c) + 1)*arctan2(sin(d*sqrt(x)), cos(d*sqrt(x))) + (-2*I*a*b*cos(2*d*sqrt(x) + 2*c) + 2*a*b*sin(2*d*sqrt(x) + 2*c) - 2*I*a*b)*arctan2(sin(d*sqrt(x)), cos(d*sqrt(x)))*log(cos(2*d*sqrt(x) - 2*c)^2 + sin(2*d*sqrt(x) - 2*c)^2 + 2*cos(2*d*sqrt(x) - 2*c) + 1) - ((2*a*b - I*b^2)*d^2*cos(2*d*sqrt(x) + 2*c) - (-2*I*a*b - b^2)*d^2*sin(2*d*sqrt(x) + 2*c) + (2*a*b - I*b^2)*d^2)*x + (2*b^2*cos(2*d*sqrt(x) + 2*c) + 2*I*b^2*sin(2*d*sqrt(x) + 2*c) + 2*b^2)*arctan2(sin(2*d*sqrt(x)) + sin(2*c), cos(2*d*sqrt(x)) + cos(2*c)) - 2*(a*b*cos(2*d*sqrt(x) + 2*c) + I*a*b*sin(2*d*sqrt(x) + 2*c) + a*b)*dilog(-e^(2*I*d*sqrt(x) - 2*I*c)) + (-I*b^2*cos(2*d*sqrt(x) + 2*c) + b^2*sin(2*d*sqrt(x) + 2*c) - I*b^2)*log(cos(2*d*sqrt(x))^2 + 2*cos(2*d*sqrt(x))*cos(2*c) + cos(2*c)^2 + sin(2*d*sqrt(x))^2 + 2*sin(2*d*sqrt(x))*sin(2*c) + sin(2*c)^2))/(-I*d^2*cos(2*d*sqrt(x) + 2*c) + d^2*sin(2*d*sqrt(x) + 2*c) - I*d^2)","B",0
34,0,0,0,0.000000," ","integrate((a+b*tan(c+d*x^(1/2)))^2/x,x, algorithm=""maxima"")","\frac{4 \, b^{2} \sqrt{x} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + 2 \, {\left(d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + d\right)} x \int \frac{2 \, a b d x \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + b^{2} \sqrt{x} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)}{{\left(d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + d\right)} x^{2}}\,{d x} + {\left({\left(a^{2} - b^{2}\right)} d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + {\left(a^{2} - b^{2}\right)} d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, {\left(a^{2} - b^{2}\right)} d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(a^{2} - b^{2}\right)} d\right)} x \log\left(x\right)}{{\left(d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + d\right)} x}"," ",0,"(4*b^2*sqrt(x)*sin(2*d*sqrt(x) + 2*c) + (d*cos(2*d*sqrt(x) + 2*c)^2 + d*sin(2*d*sqrt(x) + 2*c)^2 + 2*d*cos(2*d*sqrt(x) + 2*c) + d)*x*integrate(2*(2*a*b*d*x*sin(2*d*sqrt(x) + 2*c) + b^2*sqrt(x)*sin(2*d*sqrt(x) + 2*c))/((d*cos(2*d*sqrt(x) + 2*c)^2 + d*sin(2*d*sqrt(x) + 2*c)^2 + 2*d*cos(2*d*sqrt(x) + 2*c) + d)*x^2), x) + ((a^2 - b^2)*d*cos(2*d*sqrt(x) + 2*c)^2 + (a^2 - b^2)*d*sin(2*d*sqrt(x) + 2*c)^2 + 2*(a^2 - b^2)*d*cos(2*d*sqrt(x) + 2*c) + (a^2 - b^2)*d)*x*log(x))/((d*cos(2*d*sqrt(x) + 2*c)^2 + d*sin(2*d*sqrt(x) + 2*c)^2 + 2*d*cos(2*d*sqrt(x) + 2*c) + d)*x)","F",0
35,0,0,0,0.000000," ","integrate((a+b*tan(c+d*x^(1/2)))^2/x^2,x, algorithm=""maxima"")","\frac{2 \, {\left(d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + d\right)} x^{2} \int \frac{2 \, a b d x \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + 3 \, b^{2} \sqrt{x} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)}{{\left(d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + d\right)} x^{3}}\,{d x} + 4 \, b^{2} \sqrt{x} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left({\left(a^{2} - b^{2}\right)} d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + {\left(a^{2} - b^{2}\right)} d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, {\left(a^{2} - b^{2}\right)} d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(a^{2} - b^{2}\right)} d\right)} x}{{\left(d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + d\right)} x^{2}}"," ",0,"((d*cos(2*d*sqrt(x) + 2*c)^2 + d*sin(2*d*sqrt(x) + 2*c)^2 + 2*d*cos(2*d*sqrt(x) + 2*c) + d)*x^2*integrate(2*(2*a*b*d*x*sin(2*d*sqrt(x) + 2*c) + 3*b^2*sqrt(x)*sin(2*d*sqrt(x) + 2*c))/((d*cos(2*d*sqrt(x) + 2*c)^2 + d*sin(2*d*sqrt(x) + 2*c)^2 + 2*d*cos(2*d*sqrt(x) + 2*c) + d)*x^3), x) + 4*b^2*sqrt(x)*sin(2*d*sqrt(x) + 2*c) - ((a^2 - b^2)*d*cos(2*d*sqrt(x) + 2*c)^2 + (a^2 - b^2)*d*sin(2*d*sqrt(x) + 2*c)^2 + 2*(a^2 - b^2)*d*cos(2*d*sqrt(x) + 2*c) + (a^2 - b^2)*d)*x)/((d*cos(2*d*sqrt(x) + 2*c)^2 + d*sin(2*d*sqrt(x) + 2*c)^2 + 2*d*cos(2*d*sqrt(x) + 2*c) + d)*x^2)","F",0
36,1,1129,0,1.420236," ","integrate(x^3/(a+b*tan(c+d*x^(1/2))),x, algorithm=""maxima"")","-\frac{420 \, {\left(\frac{2 \, {\left(d \sqrt{x} + c\right)} a}{a^{2} + b^{2}} + \frac{2 \, b \log\left(b \tan\left(d \sqrt{x} + c\right) + a\right)}{a^{2} + b^{2}} - \frac{b \log\left(\tan\left(d \sqrt{x} + c\right)^{2} + 1\right)}{a^{2} + b^{2}}\right)} c^{7} - \frac{105 \, {\left(d \sqrt{x} + c\right)}^{8} {\left(a - i \, b\right)} - 840 \, {\left(d \sqrt{x} + c\right)}^{7} {\left(a - i \, b\right)} c + 2940 \, {\left(d \sqrt{x} + c\right)}^{6} {\left(a - i \, b\right)} c^{2} - 5880 \, {\left(d \sqrt{x} + c\right)}^{5} {\left(a - i \, b\right)} c^{3} + 7350 \, {\left(d \sqrt{x} + c\right)}^{4} {\left(a - i \, b\right)} c^{4} - 5880 \, {\left(d \sqrt{x} + c\right)}^{3} {\left(a - i \, b\right)} c^{5} + 2940 \, {\left(d \sqrt{x} + c\right)}^{2} {\left(a - i \, b\right)} c^{6} + {\left(-7680 i \, {\left(d \sqrt{x} + c\right)}^{7} b + 31360 i \, {\left(d \sqrt{x} + c\right)}^{6} b c - 56448 i \, {\left(d \sqrt{x} + c\right)}^{5} b c^{2} + 58800 i \, {\left(d \sqrt{x} + c\right)}^{4} b c^{3} - 39200 i \, {\left(d \sqrt{x} + c\right)}^{3} b c^{4} + 17640 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{5} - 5880 i \, {\left(d \sqrt{x} + c\right)} b c^{6}\right)} \arctan\left(\frac{2 \, a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(a^{2} - b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)}{a^{2} + b^{2}}, \frac{2 \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + a^{2} + b^{2} + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right)}{a^{2} + b^{2}}\right) + {\left(-26880 i \, {\left(d \sqrt{x} + c\right)}^{6} b + 94080 i \, {\left(d \sqrt{x} + c\right)}^{5} b c - 141120 i \, {\left(d \sqrt{x} + c\right)}^{4} b c^{2} + 117600 i \, {\left(d \sqrt{x} + c\right)}^{3} b c^{3} - 58800 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{4} + 17640 i \, {\left(d \sqrt{x} + c\right)} b c^{5} - 2940 i \, b c^{6}\right)} {\rm Li}_2\left(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}}{-i \, a + b}\right) + 4 \, {\left(960 \, {\left(d \sqrt{x} + c\right)}^{7} b - 3920 \, {\left(d \sqrt{x} + c\right)}^{6} b c + 7056 \, {\left(d \sqrt{x} + c\right)}^{5} b c^{2} - 7350 \, {\left(d \sqrt{x} + c\right)}^{4} b c^{3} + 4900 \, {\left(d \sqrt{x} + c\right)}^{3} b c^{4} - 2205 \, {\left(d \sqrt{x} + c\right)}^{2} b c^{5} + 735 \, {\left(d \sqrt{x} + c\right)} b c^{6}\right)} \log\left(\frac{{\left(a^{2} + b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 4 \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right)}{a^{2} + b^{2}}\right) + 302400 i \, b {\rm Li}_{8}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}}{-i \, a + b}) + 50400 \, {\left(12 \, {\left(d \sqrt{x} + c\right)} b - 7 \, b c\right)} {\rm Li}_{7}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}}{-i \, a + b}) + {\left(-604800 i \, {\left(d \sqrt{x} + c\right)}^{2} b + 705600 i \, {\left(d \sqrt{x} + c\right)} b c - 211680 i \, b c^{2}\right)} {\rm Li}_{6}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}}{-i \, a + b}) - 2520 \, {\left(160 \, {\left(d \sqrt{x} + c\right)}^{3} b - 280 \, {\left(d \sqrt{x} + c\right)}^{2} b c + 168 \, {\left(d \sqrt{x} + c\right)} b c^{2} - 35 \, b c^{3}\right)} {\rm Li}_{5}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}}{-i \, a + b}) + {\left(201600 i \, {\left(d \sqrt{x} + c\right)}^{4} b - 470400 i \, {\left(d \sqrt{x} + c\right)}^{3} b c + 423360 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{2} - 176400 i \, {\left(d \sqrt{x} + c\right)} b c^{3} + 29400 i \, b c^{4}\right)} {\rm Li}_{4}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}}{-i \, a + b}) + 420 \, {\left(192 \, {\left(d \sqrt{x} + c\right)}^{5} b - 560 \, {\left(d \sqrt{x} + c\right)}^{4} b c + 672 \, {\left(d \sqrt{x} + c\right)}^{3} b c^{2} - 420 \, {\left(d \sqrt{x} + c\right)}^{2} b c^{3} + 140 \, {\left(d \sqrt{x} + c\right)} b c^{4} - 21 \, b c^{5}\right)} {\rm Li}_{3}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}}{-i \, a + b})}{a^{2} + b^{2}}}{420 \, d^{8}}"," ",0,"-1/420*(420*(2*(d*sqrt(x) + c)*a/(a^2 + b^2) + 2*b*log(b*tan(d*sqrt(x) + c) + a)/(a^2 + b^2) - b*log(tan(d*sqrt(x) + c)^2 + 1)/(a^2 + b^2))*c^7 - (105*(d*sqrt(x) + c)^8*(a - I*b) - 840*(d*sqrt(x) + c)^7*(a - I*b)*c + 2940*(d*sqrt(x) + c)^6*(a - I*b)*c^2 - 5880*(d*sqrt(x) + c)^5*(a - I*b)*c^3 + 7350*(d*sqrt(x) + c)^4*(a - I*b)*c^4 - 5880*(d*sqrt(x) + c)^3*(a - I*b)*c^5 + 2940*(d*sqrt(x) + c)^2*(a - I*b)*c^6 + (-7680*I*(d*sqrt(x) + c)^7*b + 31360*I*(d*sqrt(x) + c)^6*b*c - 56448*I*(d*sqrt(x) + c)^5*b*c^2 + 58800*I*(d*sqrt(x) + c)^4*b*c^3 - 39200*I*(d*sqrt(x) + c)^3*b*c^4 + 17640*I*(d*sqrt(x) + c)^2*b*c^5 - 5880*I*(d*sqrt(x) + c)*b*c^6)*arctan2((2*a*b*cos(2*d*sqrt(x) + 2*c) - (a^2 - b^2)*sin(2*d*sqrt(x) + 2*c))/(a^2 + b^2), (2*a*b*sin(2*d*sqrt(x) + 2*c) + a^2 + b^2 + (a^2 - b^2)*cos(2*d*sqrt(x) + 2*c))/(a^2 + b^2)) + (-26880*I*(d*sqrt(x) + c)^6*b + 94080*I*(d*sqrt(x) + c)^5*b*c - 141120*I*(d*sqrt(x) + c)^4*b*c^2 + 117600*I*(d*sqrt(x) + c)^3*b*c^3 - 58800*I*(d*sqrt(x) + c)^2*b*c^4 + 17640*I*(d*sqrt(x) + c)*b*c^5 - 2940*I*b*c^6)*dilog((I*a + b)*e^(2*I*d*sqrt(x) + 2*I*c)/(-I*a + b)) + 4*(960*(d*sqrt(x) + c)^7*b - 3920*(d*sqrt(x) + c)^6*b*c + 7056*(d*sqrt(x) + c)^5*b*c^2 - 7350*(d*sqrt(x) + c)^4*b*c^3 + 4900*(d*sqrt(x) + c)^3*b*c^4 - 2205*(d*sqrt(x) + c)^2*b*c^5 + 735*(d*sqrt(x) + c)*b*c^6)*log(((a^2 + b^2)*cos(2*d*sqrt(x) + 2*c)^2 + 4*a*b*sin(2*d*sqrt(x) + 2*c) + (a^2 + b^2)*sin(2*d*sqrt(x) + 2*c)^2 + a^2 + b^2 + 2*(a^2 - b^2)*cos(2*d*sqrt(x) + 2*c))/(a^2 + b^2)) + 302400*I*b*polylog(8, (I*a + b)*e^(2*I*d*sqrt(x) + 2*I*c)/(-I*a + b)) + 50400*(12*(d*sqrt(x) + c)*b - 7*b*c)*polylog(7, (I*a + b)*e^(2*I*d*sqrt(x) + 2*I*c)/(-I*a + b)) + (-604800*I*(d*sqrt(x) + c)^2*b + 705600*I*(d*sqrt(x) + c)*b*c - 211680*I*b*c^2)*polylog(6, (I*a + b)*e^(2*I*d*sqrt(x) + 2*I*c)/(-I*a + b)) - 2520*(160*(d*sqrt(x) + c)^3*b - 280*(d*sqrt(x) + c)^2*b*c + 168*(d*sqrt(x) + c)*b*c^2 - 35*b*c^3)*polylog(5, (I*a + b)*e^(2*I*d*sqrt(x) + 2*I*c)/(-I*a + b)) + (201600*I*(d*sqrt(x) + c)^4*b - 470400*I*(d*sqrt(x) + c)^3*b*c + 423360*I*(d*sqrt(x) + c)^2*b*c^2 - 176400*I*(d*sqrt(x) + c)*b*c^3 + 29400*I*b*c^4)*polylog(4, (I*a + b)*e^(2*I*d*sqrt(x) + 2*I*c)/(-I*a + b)) + 420*(192*(d*sqrt(x) + c)^5*b - 560*(d*sqrt(x) + c)^4*b*c + 672*(d*sqrt(x) + c)^3*b*c^2 - 420*(d*sqrt(x) + c)^2*b*c^3 + 140*(d*sqrt(x) + c)*b*c^4 - 21*b*c^5)*polylog(3, (I*a + b)*e^(2*I*d*sqrt(x) + 2*I*c)/(-I*a + b)))/(a^2 + b^2))/d^8","B",0
37,1,810,0,1.074588," ","integrate(x^2/(a+b*tan(c+d*x^(1/2))),x, algorithm=""maxima"")","-\frac{15 \, {\left(\frac{2 \, {\left(d \sqrt{x} + c\right)} a}{a^{2} + b^{2}} + \frac{2 \, b \log\left(b \tan\left(d \sqrt{x} + c\right) + a\right)}{a^{2} + b^{2}} - \frac{b \log\left(\tan\left(d \sqrt{x} + c\right)^{2} + 1\right)}{a^{2} + b^{2}}\right)} c^{5} - \frac{5 \, {\left(d \sqrt{x} + c\right)}^{6} {\left(a - i \, b\right)} - 30 \, {\left(d \sqrt{x} + c\right)}^{5} {\left(a - i \, b\right)} c + 75 \, {\left(d \sqrt{x} + c\right)}^{4} {\left(a - i \, b\right)} c^{2} - 100 \, {\left(d \sqrt{x} + c\right)}^{3} {\left(a - i \, b\right)} c^{3} + 75 \, {\left(d \sqrt{x} + c\right)}^{2} {\left(a - i \, b\right)} c^{4} + {\left(-96 i \, {\left(d \sqrt{x} + c\right)}^{5} b + 300 i \, {\left(d \sqrt{x} + c\right)}^{4} b c - 400 i \, {\left(d \sqrt{x} + c\right)}^{3} b c^{2} + 300 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{3} - 150 i \, {\left(d \sqrt{x} + c\right)} b c^{4}\right)} \arctan\left(\frac{2 \, a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(a^{2} - b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)}{a^{2} + b^{2}}, \frac{2 \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + a^{2} + b^{2} + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right)}{a^{2} + b^{2}}\right) + {\left(-240 i \, {\left(d \sqrt{x} + c\right)}^{4} b + 600 i \, {\left(d \sqrt{x} + c\right)}^{3} b c - 600 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{2} + 300 i \, {\left(d \sqrt{x} + c\right)} b c^{3} - 75 i \, b c^{4}\right)} {\rm Li}_2\left(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}}{-i \, a + b}\right) + {\left(48 \, {\left(d \sqrt{x} + c\right)}^{5} b - 150 \, {\left(d \sqrt{x} + c\right)}^{4} b c + 200 \, {\left(d \sqrt{x} + c\right)}^{3} b c^{2} - 150 \, {\left(d \sqrt{x} + c\right)}^{2} b c^{3} + 75 \, {\left(d \sqrt{x} + c\right)} b c^{4}\right)} \log\left(\frac{{\left(a^{2} + b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 4 \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right)}{a^{2} + b^{2}}\right) - 360 i \, b {\rm Li}_{6}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}}{-i \, a + b}) - 90 \, {\left(8 \, {\left(d \sqrt{x} + c\right)} b - 5 \, b c\right)} {\rm Li}_{5}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}}{-i \, a + b}) + {\left(720 i \, {\left(d \sqrt{x} + c\right)}^{2} b - 900 i \, {\left(d \sqrt{x} + c\right)} b c + 300 i \, b c^{2}\right)} {\rm Li}_{4}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}}{-i \, a + b}) + 30 \, {\left(16 \, {\left(d \sqrt{x} + c\right)}^{3} b - 30 \, {\left(d \sqrt{x} + c\right)}^{2} b c + 20 \, {\left(d \sqrt{x} + c\right)} b c^{2} - 5 \, b c^{3}\right)} {\rm Li}_{3}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}}{-i \, a + b})}{a^{2} + b^{2}}}{15 \, d^{6}}"," ",0,"-1/15*(15*(2*(d*sqrt(x) + c)*a/(a^2 + b^2) + 2*b*log(b*tan(d*sqrt(x) + c) + a)/(a^2 + b^2) - b*log(tan(d*sqrt(x) + c)^2 + 1)/(a^2 + b^2))*c^5 - (5*(d*sqrt(x) + c)^6*(a - I*b) - 30*(d*sqrt(x) + c)^5*(a - I*b)*c + 75*(d*sqrt(x) + c)^4*(a - I*b)*c^2 - 100*(d*sqrt(x) + c)^3*(a - I*b)*c^3 + 75*(d*sqrt(x) + c)^2*(a - I*b)*c^4 + (-96*I*(d*sqrt(x) + c)^5*b + 300*I*(d*sqrt(x) + c)^4*b*c - 400*I*(d*sqrt(x) + c)^3*b*c^2 + 300*I*(d*sqrt(x) + c)^2*b*c^3 - 150*I*(d*sqrt(x) + c)*b*c^4)*arctan2((2*a*b*cos(2*d*sqrt(x) + 2*c) - (a^2 - b^2)*sin(2*d*sqrt(x) + 2*c))/(a^2 + b^2), (2*a*b*sin(2*d*sqrt(x) + 2*c) + a^2 + b^2 + (a^2 - b^2)*cos(2*d*sqrt(x) + 2*c))/(a^2 + b^2)) + (-240*I*(d*sqrt(x) + c)^4*b + 600*I*(d*sqrt(x) + c)^3*b*c - 600*I*(d*sqrt(x) + c)^2*b*c^2 + 300*I*(d*sqrt(x) + c)*b*c^3 - 75*I*b*c^4)*dilog((I*a + b)*e^(2*I*d*sqrt(x) + 2*I*c)/(-I*a + b)) + (48*(d*sqrt(x) + c)^5*b - 150*(d*sqrt(x) + c)^4*b*c + 200*(d*sqrt(x) + c)^3*b*c^2 - 150*(d*sqrt(x) + c)^2*b*c^3 + 75*(d*sqrt(x) + c)*b*c^4)*log(((a^2 + b^2)*cos(2*d*sqrt(x) + 2*c)^2 + 4*a*b*sin(2*d*sqrt(x) + 2*c) + (a^2 + b^2)*sin(2*d*sqrt(x) + 2*c)^2 + a^2 + b^2 + 2*(a^2 - b^2)*cos(2*d*sqrt(x) + 2*c))/(a^2 + b^2)) - 360*I*b*polylog(6, (I*a + b)*e^(2*I*d*sqrt(x) + 2*I*c)/(-I*a + b)) - 90*(8*(d*sqrt(x) + c)*b - 5*b*c)*polylog(5, (I*a + b)*e^(2*I*d*sqrt(x) + 2*I*c)/(-I*a + b)) + (720*I*(d*sqrt(x) + c)^2*b - 900*I*(d*sqrt(x) + c)*b*c + 300*I*b*c^2)*polylog(4, (I*a + b)*e^(2*I*d*sqrt(x) + 2*I*c)/(-I*a + b)) + 30*(16*(d*sqrt(x) + c)^3*b - 30*(d*sqrt(x) + c)^2*b*c + 20*(d*sqrt(x) + c)*b*c^2 - 5*b*c^3)*polylog(3, (I*a + b)*e^(2*I*d*sqrt(x) + 2*I*c)/(-I*a + b)))/(a^2 + b^2))/d^6","B",0
38,1,553,0,1.016481," ","integrate(x/(a+b*tan(c+d*x^(1/2))),x, algorithm=""maxima"")","-\frac{6 \, {\left(\frac{2 \, {\left(d \sqrt{x} + c\right)} a}{a^{2} + b^{2}} + \frac{2 \, b \log\left(b \tan\left(d \sqrt{x} + c\right) + a\right)}{a^{2} + b^{2}} - \frac{b \log\left(\tan\left(d \sqrt{x} + c\right)^{2} + 1\right)}{a^{2} + b^{2}}\right)} c^{3} - \frac{3 \, {\left(d \sqrt{x} + c\right)}^{4} {\left(a - i \, b\right)} - 12 \, {\left(d \sqrt{x} + c\right)}^{3} {\left(a - i \, b\right)} c + 18 \, {\left(d \sqrt{x} + c\right)}^{2} {\left(a - i \, b\right)} c^{2} + {\left(-16 i \, {\left(d \sqrt{x} + c\right)}^{3} b + 36 i \, {\left(d \sqrt{x} + c\right)}^{2} b c - 36 i \, {\left(d \sqrt{x} + c\right)} b c^{2}\right)} \arctan\left(\frac{2 \, a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(a^{2} - b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)}{a^{2} + b^{2}}, \frac{2 \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + a^{2} + b^{2} + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right)}{a^{2} + b^{2}}\right) + {\left(-24 i \, {\left(d \sqrt{x} + c\right)}^{2} b + 36 i \, {\left(d \sqrt{x} + c\right)} b c - 18 i \, b c^{2}\right)} {\rm Li}_2\left(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}}{-i \, a + b}\right) + 2 \, {\left(4 \, {\left(d \sqrt{x} + c\right)}^{3} b - 9 \, {\left(d \sqrt{x} + c\right)}^{2} b c + 9 \, {\left(d \sqrt{x} + c\right)} b c^{2}\right)} \log\left(\frac{{\left(a^{2} + b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 4 \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right)}{a^{2} + b^{2}}\right) + 12 i \, b {\rm Li}_{4}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}}{-i \, a + b}) + 6 \, {\left(4 \, {\left(d \sqrt{x} + c\right)} b - 3 \, b c\right)} {\rm Li}_{3}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}}{-i \, a + b})}{a^{2} + b^{2}}}{6 \, d^{4}}"," ",0,"-1/6*(6*(2*(d*sqrt(x) + c)*a/(a^2 + b^2) + 2*b*log(b*tan(d*sqrt(x) + c) + a)/(a^2 + b^2) - b*log(tan(d*sqrt(x) + c)^2 + 1)/(a^2 + b^2))*c^3 - (3*(d*sqrt(x) + c)^4*(a - I*b) - 12*(d*sqrt(x) + c)^3*(a - I*b)*c + 18*(d*sqrt(x) + c)^2*(a - I*b)*c^2 + (-16*I*(d*sqrt(x) + c)^3*b + 36*I*(d*sqrt(x) + c)^2*b*c - 36*I*(d*sqrt(x) + c)*b*c^2)*arctan2((2*a*b*cos(2*d*sqrt(x) + 2*c) - (a^2 - b^2)*sin(2*d*sqrt(x) + 2*c))/(a^2 + b^2), (2*a*b*sin(2*d*sqrt(x) + 2*c) + a^2 + b^2 + (a^2 - b^2)*cos(2*d*sqrt(x) + 2*c))/(a^2 + b^2)) + (-24*I*(d*sqrt(x) + c)^2*b + 36*I*(d*sqrt(x) + c)*b*c - 18*I*b*c^2)*dilog((I*a + b)*e^(2*I*d*sqrt(x) + 2*I*c)/(-I*a + b)) + 2*(4*(d*sqrt(x) + c)^3*b - 9*(d*sqrt(x) + c)^2*b*c + 9*(d*sqrt(x) + c)*b*c^2)*log(((a^2 + b^2)*cos(2*d*sqrt(x) + 2*c)^2 + 4*a*b*sin(2*d*sqrt(x) + 2*c) + (a^2 + b^2)*sin(2*d*sqrt(x) + 2*c)^2 + a^2 + b^2 + 2*(a^2 - b^2)*cos(2*d*sqrt(x) + 2*c))/(a^2 + b^2)) + 12*I*b*polylog(4, (I*a + b)*e^(2*I*d*sqrt(x) + 2*I*c)/(-I*a + b)) + 6*(4*(d*sqrt(x) + c)*b - 3*b*c)*polylog(3, (I*a + b)*e^(2*I*d*sqrt(x) + 2*I*c)/(-I*a + b)))/(a^2 + b^2))/d^4","B",0
39,1,264,0,0.736180," ","integrate(1/(a+b*tan(c+d*x^(1/2))),x, algorithm=""maxima"")","\frac{{\left(a - i \, b\right)} d^{2} x - 2 i \, b d \sqrt{x} \arctan\left(\frac{2 \, a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(a^{2} - b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)}{a^{2} + b^{2}}, \frac{2 \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + a^{2} + b^{2} + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right)}{a^{2} + b^{2}}\right) + b d \sqrt{x} \log\left(\frac{{\left(a^{2} + b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 4 \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right)}{a^{2} + b^{2}}\right) - i \, b {\rm Li}_2\left(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}}{-i \, a + b}\right)}{{\left(a^{2} + b^{2}\right)} d^{2}}"," ",0,"((a - I*b)*d^2*x - 2*I*b*d*sqrt(x)*arctan2((2*a*b*cos(2*d*sqrt(x) + 2*c) - (a^2 - b^2)*sin(2*d*sqrt(x) + 2*c))/(a^2 + b^2), (2*a*b*sin(2*d*sqrt(x) + 2*c) + a^2 + b^2 + (a^2 - b^2)*cos(2*d*sqrt(x) + 2*c))/(a^2 + b^2)) + b*d*sqrt(x)*log(((a^2 + b^2)*cos(2*d*sqrt(x) + 2*c)^2 + 4*a*b*sin(2*d*sqrt(x) + 2*c) + (a^2 + b^2)*sin(2*d*sqrt(x) + 2*c)^2 + a^2 + b^2 + 2*(a^2 - b^2)*cos(2*d*sqrt(x) + 2*c))/(a^2 + b^2)) - I*b*dilog((I*a + b)*e^(2*I*d*sqrt(x) + 2*I*c)/(-I*a + b)))/((a^2 + b^2)*d^2)","B",0
40,-1,0,0,0.000000," ","integrate(1/x/(a+b*tan(c+d*x^(1/2))),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
41,-1,0,0,0.000000," ","integrate(1/x^2/(a+b*tan(c+d*x^(1/2))),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
42,1,4349,0,3.442909," ","integrate(x^2/(a+b*tan(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(\frac{2 \, a b \log\left(b \tan\left(d \sqrt{x} + c\right) + a\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{a b \log\left(\tan\left(d \sqrt{x} + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(a^{2} - b^{2}\right)} {\left(d \sqrt{x} + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{b}{a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} \tan\left(d \sqrt{x} + c\right)}\right)} c^{5} - \frac{{\left(5 \, a^{3} - 5 i \, a^{2} b + 5 \, a b^{2} - 5 i \, b^{3}\right)} {\left(d \sqrt{x} + c\right)}^{6} - {\left(30 \, a^{3} - 30 i \, a^{2} b + 30 \, a b^{2} - 30 i \, b^{3}\right)} {\left(d \sqrt{x} + c\right)}^{5} c + {\left(75 \, a^{3} - 75 i \, a^{2} b + 75 \, a b^{2} - 75 i \, b^{3}\right)} {\left(d \sqrt{x} + c\right)}^{4} c^{2} - {\left(100 \, a^{3} - 100 i \, a^{2} b + 100 \, a b^{2} - 100 i \, b^{3}\right)} {\left(d \sqrt{x} + c\right)}^{3} c^{3} + {\left(75 \, a^{3} - 75 i \, a^{2} b + 75 \, a b^{2} - 75 i \, b^{3}\right)} {\left(d \sqrt{x} + c\right)}^{2} c^{4} + {\left({\left(150 i \, a b^{2} + 150 \, b^{3}\right)} c^{4} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 150 \, {\left(a b^{2} - i \, b^{3}\right)} c^{4} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(150 i \, a b^{2} - 150 \, b^{3}\right)} c^{4}\right)} \arctan\left(-b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + a \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + b, a \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + a\right) + {\left({\left(-192 i \, a^{2} b + 192 \, a b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{5} + {\left(-300 i \, a b^{2} + 300 \, b^{3} + {\left(600 i \, a^{2} b - 600 \, a b^{2}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left({\left(-800 i \, a^{2} b + 800 \, a b^{2}\right)} c^{2} + {\left(800 i \, a b^{2} - 800 \, b^{3}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left({\left(600 i \, a^{2} b - 600 \, a b^{2}\right)} c^{3} + {\left(-900 i \, a b^{2} + 900 \, b^{3}\right)} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left({\left(-300 i \, a^{2} b + 300 \, a b^{2}\right)} c^{4} + {\left(600 i \, a b^{2} - 600 \, b^{3}\right)} c^{3}\right)} {\left(d \sqrt{x} + c\right)} + {\left({\left(-192 i \, a^{2} b - 192 \, a b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{5} + {\left(-300 i \, a b^{2} - 300 \, b^{3} + {\left(600 i \, a^{2} b + 600 \, a b^{2}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left({\left(-800 i \, a^{2} b - 800 \, a b^{2}\right)} c^{2} + {\left(800 i \, a b^{2} + 800 \, b^{3}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left({\left(600 i \, a^{2} b + 600 \, a b^{2}\right)} c^{3} + {\left(-900 i \, a b^{2} - 900 \, b^{3}\right)} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left({\left(-300 i \, a^{2} b - 300 \, a b^{2}\right)} c^{4} + {\left(600 i \, a b^{2} + 600 \, b^{3}\right)} c^{3}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 4 \, {\left(48 \, {\left(a^{2} b - i \, a b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{5} + 75 \, {\left(a b^{2} - i \, b^{3} - 2 \, {\left(a^{2} b - i \, a b^{2}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{4} + 200 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} c^{2} - {\left(a b^{2} - i \, b^{3}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{3} - 75 \, {\left(2 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{3} - 3 \, {\left(a b^{2} - i \, b^{3}\right)} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 75 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} c^{4} - 2 \, {\left(a b^{2} - i \, b^{3}\right)} c^{3}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \arctan\left(\frac{2 \, a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(a^{2} - b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)}{a^{2} + b^{2}}, \frac{2 \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + a^{2} + b^{2} + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right)}{a^{2} + b^{2}}\right) + {\left({\left(5 \, a^{3} - 15 i \, a^{2} b - 15 \, a b^{2} + 5 i \, b^{3}\right)} {\left(d \sqrt{x} + c\right)}^{6} + {\left(-60 i \, a b^{2} - 60 \, b^{3} - {\left(30 \, a^{3} - 90 i \, a^{2} b - 90 \, a b^{2} + 30 i \, b^{3}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{5} + {\left(-300 i \, a b^{2} - 300 \, b^{3}\right)} {\left(d \sqrt{x} + c\right)} c^{4} + {\left({\left(75 \, a^{3} - 225 i \, a^{2} b - 225 \, a b^{2} + 75 i \, b^{3}\right)} c^{2} + {\left(300 i \, a b^{2} + 300 \, b^{3}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{4} - {\left({\left(100 \, a^{3} - 300 i \, a^{2} b - 300 \, a b^{2} + 100 i \, b^{3}\right)} c^{3} - {\left(-600 i \, a b^{2} - 600 \, b^{3}\right)} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left({\left(75 \, a^{3} - 225 i \, a^{2} b - 225 \, a b^{2} + 75 i \, b^{3}\right)} c^{4} + {\left(600 i \, a b^{2} + 600 \, b^{3}\right)} c^{3}\right)} {\left(d \sqrt{x} + c\right)}^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left({\left(-480 i \, a^{2} b + 480 \, a b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left(-150 i \, a^{2} b + 150 \, a b^{2}\right)} c^{4} + {\left(-600 i \, a b^{2} + 600 \, b^{3} + {\left(1200 i \, a^{2} b - 1200 \, a b^{2}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(300 i \, a b^{2} - 300 \, b^{3}\right)} c^{3} + {\left({\left(-1200 i \, a^{2} b + 1200 \, a b^{2}\right)} c^{2} + {\left(1200 i \, a b^{2} - 1200 \, b^{3}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left({\left(600 i \, a^{2} b - 600 \, a b^{2}\right)} c^{3} + {\left(-900 i \, a b^{2} + 900 \, b^{3}\right)} c^{2}\right)} {\left(d \sqrt{x} + c\right)} + {\left({\left(-480 i \, a^{2} b - 480 \, a b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left(-150 i \, a^{2} b - 150 \, a b^{2}\right)} c^{4} + {\left(-600 i \, a b^{2} - 600 \, b^{3} + {\left(1200 i \, a^{2} b + 1200 \, a b^{2}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(300 i \, a b^{2} + 300 \, b^{3}\right)} c^{3} + {\left({\left(-1200 i \, a^{2} b - 1200 \, a b^{2}\right)} c^{2} + {\left(1200 i \, a b^{2} + 1200 \, b^{3}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left({\left(600 i \, a^{2} b + 600 \, a b^{2}\right)} c^{3} + {\left(-900 i \, a b^{2} - 900 \, b^{3}\right)} c^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 30 \, {\left(16 \, {\left(a^{2} b - i \, a b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{4} + 5 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{4} + 20 \, {\left(a b^{2} - i \, b^{3} - 2 \, {\left(a^{2} b - i \, a b^{2}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{3} - 10 \, {\left(a b^{2} - i \, b^{3}\right)} c^{3} + 40 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} c^{2} - {\left(a b^{2} - i \, b^{3}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{2} - 10 \, {\left(2 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{3} - 3 \, {\left(a b^{2} - i \, b^{3}\right)} c^{2}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_2\left(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}}{-i \, a + b}\right) + {\left(75 \, {\left(a b^{2} - i \, b^{3}\right)} c^{4} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(75 i \, a b^{2} + 75 \, b^{3}\right)} c^{4} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + 75 \, {\left(a b^{2} + i \, b^{3}\right)} c^{4}\right)} \log\left({\left(a^{2} + b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 4 \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right)\right) + {\left(96 \, {\left(a^{2} b + i \, a b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{5} + 150 \, {\left(a b^{2} + i \, b^{3} - 2 \, {\left(a^{2} b + i \, a b^{2}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{4} + 400 \, {\left({\left(a^{2} b + i \, a b^{2}\right)} c^{2} - {\left(a b^{2} + i \, b^{3}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{3} - 150 \, {\left(2 \, {\left(a^{2} b + i \, a b^{2}\right)} c^{3} - 3 \, {\left(a b^{2} + i \, b^{3}\right)} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 150 \, {\left({\left(a^{2} b + i \, a b^{2}\right)} c^{4} - 2 \, {\left(a b^{2} + i \, b^{3}\right)} c^{3}\right)} {\left(d \sqrt{x} + c\right)} + 2 \, {\left(48 \, {\left(a^{2} b - i \, a b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{5} + 75 \, {\left(a b^{2} - i \, b^{3} - 2 \, {\left(a^{2} b - i \, a b^{2}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{4} + 200 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} c^{2} - {\left(a b^{2} - i \, b^{3}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{3} - 75 \, {\left(2 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{3} - 3 \, {\left(a b^{2} - i \, b^{3}\right)} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 75 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} c^{4} - 2 \, {\left(a b^{2} - i \, b^{3}\right)} c^{3}\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left({\left(96 i \, a^{2} b + 96 \, a b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{5} + {\left(150 i \, a b^{2} + 150 \, b^{3} + {\left(-300 i \, a^{2} b - 300 \, a b^{2}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left({\left(400 i \, a^{2} b + 400 \, a b^{2}\right)} c^{2} + {\left(-400 i \, a b^{2} - 400 \, b^{3}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left({\left(-300 i \, a^{2} b - 300 \, a b^{2}\right)} c^{3} + {\left(450 i \, a b^{2} + 450 \, b^{3}\right)} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left({\left(150 i \, a^{2} b + 150 \, a b^{2}\right)} c^{4} + {\left(-300 i \, a b^{2} - 300 \, b^{3}\right)} c^{3}\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \log\left(\frac{{\left(a^{2} + b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 4 \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right)}{a^{2} + b^{2}}\right) + {\left(-720 i \, a^{2} b + 720 \, a b^{2} + {\left(-720 i \, a^{2} b - 720 \, a b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 720 \, {\left(a^{2} b - i \, a b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{6}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}}{-i \, a + b}) - {\left(450 \, a b^{2} + 450 i \, b^{3} + 1440 \, {\left(a^{2} b + i \, a b^{2}\right)} {\left(d \sqrt{x} + c\right)} - 900 \, {\left(a^{2} b + i \, a b^{2}\right)} c + {\left(450 \, a b^{2} - 450 i \, b^{3} + 1440 \, {\left(a^{2} b - i \, a b^{2}\right)} {\left(d \sqrt{x} + c\right)} - 900 \, {\left(a^{2} b - i \, a b^{2}\right)} c\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(-450 i \, a b^{2} - 450 \, b^{3} + {\left(-1440 i \, a^{2} b - 1440 \, a b^{2}\right)} {\left(d \sqrt{x} + c\right)} + {\left(900 i \, a^{2} b + 900 \, a b^{2}\right)} c\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{5}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}}{-i \, a + b}) + {\left({\left(1440 i \, a^{2} b - 1440 \, a b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(600 i \, a^{2} b - 600 \, a b^{2}\right)} c^{2} + {\left(900 i \, a b^{2} - 900 \, b^{3} + {\left(-1800 i \, a^{2} b + 1800 \, a b^{2}\right)} c\right)} {\left(d \sqrt{x} + c\right)} + {\left(-600 i \, a b^{2} + 600 \, b^{3}\right)} c + {\left({\left(1440 i \, a^{2} b + 1440 \, a b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(600 i \, a^{2} b + 600 \, a b^{2}\right)} c^{2} + {\left(900 i \, a b^{2} + 900 \, b^{3} + {\left(-1800 i \, a^{2} b - 1800 \, a b^{2}\right)} c\right)} {\left(d \sqrt{x} + c\right)} + {\left(-600 i \, a b^{2} - 600 \, b^{3}\right)} c\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 60 \, {\left(24 \, {\left(a^{2} b - i \, a b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 10 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{2} + 15 \, {\left(a b^{2} - i \, b^{3} - 2 \, {\left(a^{2} b - i \, a b^{2}\right)} c\right)} {\left(d \sqrt{x} + c\right)} - 10 \, {\left(a b^{2} - i \, b^{3}\right)} c\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{4}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}}{-i \, a + b}) + {\left(960 \, {\left(a^{2} b + i \, a b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} - 300 \, {\left(a^{2} b + i \, a b^{2}\right)} c^{3} + 900 \, {\left(a b^{2} + i \, b^{3} - 2 \, {\left(a^{2} b + i \, a b^{2}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{2} + 450 \, {\left(a b^{2} + i \, b^{3}\right)} c^{2} + 1200 \, {\left({\left(a^{2} b + i \, a b^{2}\right)} c^{2} - {\left(a b^{2} + i \, b^{3}\right)} c\right)} {\left(d \sqrt{x} + c\right)} + 30 \, {\left(32 \, {\left(a^{2} b - i \, a b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} - 10 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{3} + 30 \, {\left(a b^{2} - i \, b^{3} - 2 \, {\left(a^{2} b - i \, a b^{2}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{2} + 15 \, {\left(a b^{2} - i \, b^{3}\right)} c^{2} + 40 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} c^{2} - {\left(a b^{2} - i \, b^{3}\right)} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left({\left(960 i \, a^{2} b + 960 \, a b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(-300 i \, a^{2} b - 300 \, a b^{2}\right)} c^{3} + {\left(900 i \, a b^{2} + 900 \, b^{3} + {\left(-1800 i \, a^{2} b - 1800 \, a b^{2}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(450 i \, a b^{2} + 450 \, b^{3}\right)} c^{2} + {\left({\left(1200 i \, a^{2} b + 1200 \, a b^{2}\right)} c^{2} + {\left(-1200 i \, a b^{2} - 1200 \, b^{3}\right)} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{3}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}}{-i \, a + b}) + {\left({\left(5 i \, a^{3} + 15 \, a^{2} b - 15 i \, a b^{2} - 5 \, b^{3}\right)} {\left(d \sqrt{x} + c\right)}^{6} + {\left(60 \, a b^{2} - 60 i \, b^{3} + {\left(-30 i \, a^{3} - 90 \, a^{2} b + 90 i \, a b^{2} + 30 \, b^{3}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{5} + 300 \, {\left(a b^{2} - i \, b^{3}\right)} {\left(d \sqrt{x} + c\right)} c^{4} + {\left({\left(75 i \, a^{3} + 225 \, a^{2} b - 225 i \, a b^{2} - 75 \, b^{3}\right)} c^{2} - 300 \, {\left(a b^{2} - i \, b^{3}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left({\left(-100 i \, a^{3} - 300 \, a^{2} b + 300 i \, a b^{2} + 100 \, b^{3}\right)} c^{3} + 600 \, {\left(a b^{2} - i \, b^{3}\right)} c^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left({\left(75 i \, a^{3} + 225 \, a^{2} b - 225 i \, a b^{2} - 75 \, b^{3}\right)} c^{4} - 600 \, {\left(a b^{2} - i \, b^{3}\right)} c^{3}\right)} {\left(d \sqrt{x} + c\right)}^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)}{30 \, a^{5} + 30 i \, a^{4} b + 60 \, a^{3} b^{2} + 60 i \, a^{2} b^{3} + 30 \, a b^{4} + 30 i \, b^{5} + {\left(30 \, a^{5} - 30 i \, a^{4} b + 60 \, a^{3} b^{2} - 60 i \, a^{2} b^{3} + 30 \, a b^{4} - 30 i \, b^{5}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(30 i \, a^{5} + 30 \, a^{4} b + 60 i \, a^{3} b^{2} + 60 \, a^{2} b^{3} + 30 i \, a b^{4} + 30 \, b^{5}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)}\right)}}{d^{6}}"," ",0,"-2*((2*a*b*log(b*tan(d*sqrt(x) + c) + a)/(a^4 + 2*a^2*b^2 + b^4) - a*b*log(tan(d*sqrt(x) + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + (a^2 - b^2)*(d*sqrt(x) + c)/(a^4 + 2*a^2*b^2 + b^4) - b/(a^3 + a*b^2 + (a^2*b + b^3)*tan(d*sqrt(x) + c)))*c^5 - ((5*a^3 - 5*I*a^2*b + 5*a*b^2 - 5*I*b^3)*(d*sqrt(x) + c)^6 - (30*a^3 - 30*I*a^2*b + 30*a*b^2 - 30*I*b^3)*(d*sqrt(x) + c)^5*c + (75*a^3 - 75*I*a^2*b + 75*a*b^2 - 75*I*b^3)*(d*sqrt(x) + c)^4*c^2 - (100*a^3 - 100*I*a^2*b + 100*a*b^2 - 100*I*b^3)*(d*sqrt(x) + c)^3*c^3 + (75*a^3 - 75*I*a^2*b + 75*a*b^2 - 75*I*b^3)*(d*sqrt(x) + c)^2*c^4 + ((150*I*a*b^2 + 150*b^3)*c^4*cos(2*d*sqrt(x) + 2*c) - 150*(a*b^2 - I*b^3)*c^4*sin(2*d*sqrt(x) + 2*c) + (150*I*a*b^2 - 150*b^3)*c^4)*arctan2(-b*cos(2*d*sqrt(x) + 2*c) + a*sin(2*d*sqrt(x) + 2*c) + b, a*cos(2*d*sqrt(x) + 2*c) + b*sin(2*d*sqrt(x) + 2*c) + a) + ((-192*I*a^2*b + 192*a*b^2)*(d*sqrt(x) + c)^5 + (-300*I*a*b^2 + 300*b^3 + (600*I*a^2*b - 600*a*b^2)*c)*(d*sqrt(x) + c)^4 + ((-800*I*a^2*b + 800*a*b^2)*c^2 + (800*I*a*b^2 - 800*b^3)*c)*(d*sqrt(x) + c)^3 + ((600*I*a^2*b - 600*a*b^2)*c^3 + (-900*I*a*b^2 + 900*b^3)*c^2)*(d*sqrt(x) + c)^2 + ((-300*I*a^2*b + 300*a*b^2)*c^4 + (600*I*a*b^2 - 600*b^3)*c^3)*(d*sqrt(x) + c) + ((-192*I*a^2*b - 192*a*b^2)*(d*sqrt(x) + c)^5 + (-300*I*a*b^2 - 300*b^3 + (600*I*a^2*b + 600*a*b^2)*c)*(d*sqrt(x) + c)^4 + ((-800*I*a^2*b - 800*a*b^2)*c^2 + (800*I*a*b^2 + 800*b^3)*c)*(d*sqrt(x) + c)^3 + ((600*I*a^2*b + 600*a*b^2)*c^3 + (-900*I*a*b^2 - 900*b^3)*c^2)*(d*sqrt(x) + c)^2 + ((-300*I*a^2*b - 300*a*b^2)*c^4 + (600*I*a*b^2 + 600*b^3)*c^3)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) + 4*(48*(a^2*b - I*a*b^2)*(d*sqrt(x) + c)^5 + 75*(a*b^2 - I*b^3 - 2*(a^2*b - I*a*b^2)*c)*(d*sqrt(x) + c)^4 + 200*((a^2*b - I*a*b^2)*c^2 - (a*b^2 - I*b^3)*c)*(d*sqrt(x) + c)^3 - 75*(2*(a^2*b - I*a*b^2)*c^3 - 3*(a*b^2 - I*b^3)*c^2)*(d*sqrt(x) + c)^2 + 75*((a^2*b - I*a*b^2)*c^4 - 2*(a*b^2 - I*b^3)*c^3)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*arctan2((2*a*b*cos(2*d*sqrt(x) + 2*c) - (a^2 - b^2)*sin(2*d*sqrt(x) + 2*c))/(a^2 + b^2), (2*a*b*sin(2*d*sqrt(x) + 2*c) + a^2 + b^2 + (a^2 - b^2)*cos(2*d*sqrt(x) + 2*c))/(a^2 + b^2)) + ((5*a^3 - 15*I*a^2*b - 15*a*b^2 + 5*I*b^3)*(d*sqrt(x) + c)^6 + (-60*I*a*b^2 - 60*b^3 - (30*a^3 - 90*I*a^2*b - 90*a*b^2 + 30*I*b^3)*c)*(d*sqrt(x) + c)^5 + (-300*I*a*b^2 - 300*b^3)*(d*sqrt(x) + c)*c^4 + ((75*a^3 - 225*I*a^2*b - 225*a*b^2 + 75*I*b^3)*c^2 + (300*I*a*b^2 + 300*b^3)*c)*(d*sqrt(x) + c)^4 - ((100*a^3 - 300*I*a^2*b - 300*a*b^2 + 100*I*b^3)*c^3 - (-600*I*a*b^2 - 600*b^3)*c^2)*(d*sqrt(x) + c)^3 + ((75*a^3 - 225*I*a^2*b - 225*a*b^2 + 75*I*b^3)*c^4 + (600*I*a*b^2 + 600*b^3)*c^3)*(d*sqrt(x) + c)^2)*cos(2*d*sqrt(x) + 2*c) + ((-480*I*a^2*b + 480*a*b^2)*(d*sqrt(x) + c)^4 + (-150*I*a^2*b + 150*a*b^2)*c^4 + (-600*I*a*b^2 + 600*b^3 + (1200*I*a^2*b - 1200*a*b^2)*c)*(d*sqrt(x) + c)^3 + (300*I*a*b^2 - 300*b^3)*c^3 + ((-1200*I*a^2*b + 1200*a*b^2)*c^2 + (1200*I*a*b^2 - 1200*b^3)*c)*(d*sqrt(x) + c)^2 + ((600*I*a^2*b - 600*a*b^2)*c^3 + (-900*I*a*b^2 + 900*b^3)*c^2)*(d*sqrt(x) + c) + ((-480*I*a^2*b - 480*a*b^2)*(d*sqrt(x) + c)^4 + (-150*I*a^2*b - 150*a*b^2)*c^4 + (-600*I*a*b^2 - 600*b^3 + (1200*I*a^2*b + 1200*a*b^2)*c)*(d*sqrt(x) + c)^3 + (300*I*a*b^2 + 300*b^3)*c^3 + ((-1200*I*a^2*b - 1200*a*b^2)*c^2 + (1200*I*a*b^2 + 1200*b^3)*c)*(d*sqrt(x) + c)^2 + ((600*I*a^2*b + 600*a*b^2)*c^3 + (-900*I*a*b^2 - 900*b^3)*c^2)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) + 30*(16*(a^2*b - I*a*b^2)*(d*sqrt(x) + c)^4 + 5*(a^2*b - I*a*b^2)*c^4 + 20*(a*b^2 - I*b^3 - 2*(a^2*b - I*a*b^2)*c)*(d*sqrt(x) + c)^3 - 10*(a*b^2 - I*b^3)*c^3 + 40*((a^2*b - I*a*b^2)*c^2 - (a*b^2 - I*b^3)*c)*(d*sqrt(x) + c)^2 - 10*(2*(a^2*b - I*a*b^2)*c^3 - 3*(a*b^2 - I*b^3)*c^2)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*dilog((I*a + b)*e^(2*I*d*sqrt(x) + 2*I*c)/(-I*a + b)) + (75*(a*b^2 - I*b^3)*c^4*cos(2*d*sqrt(x) + 2*c) + (75*I*a*b^2 + 75*b^3)*c^4*sin(2*d*sqrt(x) + 2*c) + 75*(a*b^2 + I*b^3)*c^4)*log((a^2 + b^2)*cos(2*d*sqrt(x) + 2*c)^2 + 4*a*b*sin(2*d*sqrt(x) + 2*c) + (a^2 + b^2)*sin(2*d*sqrt(x) + 2*c)^2 + a^2 + b^2 + 2*(a^2 - b^2)*cos(2*d*sqrt(x) + 2*c)) + (96*(a^2*b + I*a*b^2)*(d*sqrt(x) + c)^5 + 150*(a*b^2 + I*b^3 - 2*(a^2*b + I*a*b^2)*c)*(d*sqrt(x) + c)^4 + 400*((a^2*b + I*a*b^2)*c^2 - (a*b^2 + I*b^3)*c)*(d*sqrt(x) + c)^3 - 150*(2*(a^2*b + I*a*b^2)*c^3 - 3*(a*b^2 + I*b^3)*c^2)*(d*sqrt(x) + c)^2 + 150*((a^2*b + I*a*b^2)*c^4 - 2*(a*b^2 + I*b^3)*c^3)*(d*sqrt(x) + c) + 2*(48*(a^2*b - I*a*b^2)*(d*sqrt(x) + c)^5 + 75*(a*b^2 - I*b^3 - 2*(a^2*b - I*a*b^2)*c)*(d*sqrt(x) + c)^4 + 200*((a^2*b - I*a*b^2)*c^2 - (a*b^2 - I*b^3)*c)*(d*sqrt(x) + c)^3 - 75*(2*(a^2*b - I*a*b^2)*c^3 - 3*(a*b^2 - I*b^3)*c^2)*(d*sqrt(x) + c)^2 + 75*((a^2*b - I*a*b^2)*c^4 - 2*(a*b^2 - I*b^3)*c^3)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) + ((96*I*a^2*b + 96*a*b^2)*(d*sqrt(x) + c)^5 + (150*I*a*b^2 + 150*b^3 + (-300*I*a^2*b - 300*a*b^2)*c)*(d*sqrt(x) + c)^4 + ((400*I*a^2*b + 400*a*b^2)*c^2 + (-400*I*a*b^2 - 400*b^3)*c)*(d*sqrt(x) + c)^3 + ((-300*I*a^2*b - 300*a*b^2)*c^3 + (450*I*a*b^2 + 450*b^3)*c^2)*(d*sqrt(x) + c)^2 + ((150*I*a^2*b + 150*a*b^2)*c^4 + (-300*I*a*b^2 - 300*b^3)*c^3)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*log(((a^2 + b^2)*cos(2*d*sqrt(x) + 2*c)^2 + 4*a*b*sin(2*d*sqrt(x) + 2*c) + (a^2 + b^2)*sin(2*d*sqrt(x) + 2*c)^2 + a^2 + b^2 + 2*(a^2 - b^2)*cos(2*d*sqrt(x) + 2*c))/(a^2 + b^2)) + (-720*I*a^2*b + 720*a*b^2 + (-720*I*a^2*b - 720*a*b^2)*cos(2*d*sqrt(x) + 2*c) + 720*(a^2*b - I*a*b^2)*sin(2*d*sqrt(x) + 2*c))*polylog(6, (I*a + b)*e^(2*I*d*sqrt(x) + 2*I*c)/(-I*a + b)) - (450*a*b^2 + 450*I*b^3 + 1440*(a^2*b + I*a*b^2)*(d*sqrt(x) + c) - 900*(a^2*b + I*a*b^2)*c + (450*a*b^2 - 450*I*b^3 + 1440*(a^2*b - I*a*b^2)*(d*sqrt(x) + c) - 900*(a^2*b - I*a*b^2)*c)*cos(2*d*sqrt(x) + 2*c) - (-450*I*a*b^2 - 450*b^3 + (-1440*I*a^2*b - 1440*a*b^2)*(d*sqrt(x) + c) + (900*I*a^2*b + 900*a*b^2)*c)*sin(2*d*sqrt(x) + 2*c))*polylog(5, (I*a + b)*e^(2*I*d*sqrt(x) + 2*I*c)/(-I*a + b)) + ((1440*I*a^2*b - 1440*a*b^2)*(d*sqrt(x) + c)^2 + (600*I*a^2*b - 600*a*b^2)*c^2 + (900*I*a*b^2 - 900*b^3 + (-1800*I*a^2*b + 1800*a*b^2)*c)*(d*sqrt(x) + c) + (-600*I*a*b^2 + 600*b^3)*c + ((1440*I*a^2*b + 1440*a*b^2)*(d*sqrt(x) + c)^2 + (600*I*a^2*b + 600*a*b^2)*c^2 + (900*I*a*b^2 + 900*b^3 + (-1800*I*a^2*b - 1800*a*b^2)*c)*(d*sqrt(x) + c) + (-600*I*a*b^2 - 600*b^3)*c)*cos(2*d*sqrt(x) + 2*c) - 60*(24*(a^2*b - I*a*b^2)*(d*sqrt(x) + c)^2 + 10*(a^2*b - I*a*b^2)*c^2 + 15*(a*b^2 - I*b^3 - 2*(a^2*b - I*a*b^2)*c)*(d*sqrt(x) + c) - 10*(a*b^2 - I*b^3)*c)*sin(2*d*sqrt(x) + 2*c))*polylog(4, (I*a + b)*e^(2*I*d*sqrt(x) + 2*I*c)/(-I*a + b)) + (960*(a^2*b + I*a*b^2)*(d*sqrt(x) + c)^3 - 300*(a^2*b + I*a*b^2)*c^3 + 900*(a*b^2 + I*b^3 - 2*(a^2*b + I*a*b^2)*c)*(d*sqrt(x) + c)^2 + 450*(a*b^2 + I*b^3)*c^2 + 1200*((a^2*b + I*a*b^2)*c^2 - (a*b^2 + I*b^3)*c)*(d*sqrt(x) + c) + 30*(32*(a^2*b - I*a*b^2)*(d*sqrt(x) + c)^3 - 10*(a^2*b - I*a*b^2)*c^3 + 30*(a*b^2 - I*b^3 - 2*(a^2*b - I*a*b^2)*c)*(d*sqrt(x) + c)^2 + 15*(a*b^2 - I*b^3)*c^2 + 40*((a^2*b - I*a*b^2)*c^2 - (a*b^2 - I*b^3)*c)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) + ((960*I*a^2*b + 960*a*b^2)*(d*sqrt(x) + c)^3 + (-300*I*a^2*b - 300*a*b^2)*c^3 + (900*I*a*b^2 + 900*b^3 + (-1800*I*a^2*b - 1800*a*b^2)*c)*(d*sqrt(x) + c)^2 + (450*I*a*b^2 + 450*b^3)*c^2 + ((1200*I*a^2*b + 1200*a*b^2)*c^2 + (-1200*I*a*b^2 - 1200*b^3)*c)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*polylog(3, (I*a + b)*e^(2*I*d*sqrt(x) + 2*I*c)/(-I*a + b)) + ((5*I*a^3 + 15*a^2*b - 15*I*a*b^2 - 5*b^3)*(d*sqrt(x) + c)^6 + (60*a*b^2 - 60*I*b^3 + (-30*I*a^3 - 90*a^2*b + 90*I*a*b^2 + 30*b^3)*c)*(d*sqrt(x) + c)^5 + 300*(a*b^2 - I*b^3)*(d*sqrt(x) + c)*c^4 + ((75*I*a^3 + 225*a^2*b - 225*I*a*b^2 - 75*b^3)*c^2 - 300*(a*b^2 - I*b^3)*c)*(d*sqrt(x) + c)^4 + ((-100*I*a^3 - 300*a^2*b + 300*I*a*b^2 + 100*b^3)*c^3 + 600*(a*b^2 - I*b^3)*c^2)*(d*sqrt(x) + c)^3 + ((75*I*a^3 + 225*a^2*b - 225*I*a*b^2 - 75*b^3)*c^4 - 600*(a*b^2 - I*b^3)*c^3)*(d*sqrt(x) + c)^2)*sin(2*d*sqrt(x) + 2*c))/(30*a^5 + 30*I*a^4*b + 60*a^3*b^2 + 60*I*a^2*b^3 + 30*a*b^4 + 30*I*b^5 + (30*a^5 - 30*I*a^4*b + 60*a^3*b^2 - 60*I*a^2*b^3 + 30*a*b^4 - 30*I*b^5)*cos(2*d*sqrt(x) + 2*c) + (30*I*a^5 + 30*a^4*b + 60*I*a^3*b^2 + 60*a^2*b^3 + 30*I*a*b^4 + 30*b^5)*sin(2*d*sqrt(x) + 2*c)))/d^6","B",0
43,1,2484,0,2.312430," ","integrate(x/(a+b*tan(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(\frac{2 \, a b \log\left(b \tan\left(d \sqrt{x} + c\right) + a\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{a b \log\left(\tan\left(d \sqrt{x} + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(a^{2} - b^{2}\right)} {\left(d \sqrt{x} + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{b}{a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} \tan\left(d \sqrt{x} + c\right)}\right)} c^{3} - \frac{{\left(3 \, a^{3} - 3 i \, a^{2} b + 3 \, a b^{2} - 3 i \, b^{3}\right)} {\left(d \sqrt{x} + c\right)}^{4} - {\left(12 \, a^{3} - 12 i \, a^{2} b + 12 \, a b^{2} - 12 i \, b^{3}\right)} {\left(d \sqrt{x} + c\right)}^{3} c + {\left(18 \, a^{3} - 18 i \, a^{2} b + 18 \, a b^{2} - 18 i \, b^{3}\right)} {\left(d \sqrt{x} + c\right)}^{2} c^{2} + {\left({\left(36 i \, a b^{2} + 36 \, b^{3}\right)} c^{2} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 36 \, {\left(a b^{2} - i \, b^{3}\right)} c^{2} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(36 i \, a b^{2} - 36 \, b^{3}\right)} c^{2}\right)} \arctan\left(-b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + a \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + b, a \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + a\right) + {\left({\left(-32 i \, a^{2} b + 32 \, a b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(-36 i \, a b^{2} + 36 \, b^{3} + {\left(72 i \, a^{2} b - 72 \, a b^{2}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left({\left(-72 i \, a^{2} b + 72 \, a b^{2}\right)} c^{2} + {\left(72 i \, a b^{2} - 72 \, b^{3}\right)} c\right)} {\left(d \sqrt{x} + c\right)} + {\left({\left(-32 i \, a^{2} b - 32 \, a b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(-36 i \, a b^{2} - 36 \, b^{3} + {\left(72 i \, a^{2} b + 72 \, a b^{2}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left({\left(-72 i \, a^{2} b - 72 \, a b^{2}\right)} c^{2} + {\left(72 i \, a b^{2} + 72 \, b^{3}\right)} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 4 \, {\left(8 \, {\left(a^{2} b - i \, a b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + 9 \, {\left(a b^{2} - i \, b^{3} - 2 \, {\left(a^{2} b - i \, a b^{2}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{2} + 18 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} c^{2} - {\left(a b^{2} - i \, b^{3}\right)} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \arctan\left(\frac{2 \, a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(a^{2} - b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)}{a^{2} + b^{2}}, \frac{2 \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + a^{2} + b^{2} + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right)}{a^{2} + b^{2}}\right) + {\left({\left(3 \, a^{3} - 9 i \, a^{2} b - 9 \, a b^{2} + 3 i \, b^{3}\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left(-24 i \, a b^{2} - 24 \, b^{3} - {\left(12 \, a^{3} - 36 i \, a^{2} b - 36 \, a b^{2} + 12 i \, b^{3}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(-72 i \, a b^{2} - 72 \, b^{3}\right)} {\left(d \sqrt{x} + c\right)} c^{2} + {\left({\left(18 \, a^{3} - 54 i \, a^{2} b - 54 \, a b^{2} + 18 i \, b^{3}\right)} c^{2} + {\left(72 i \, a b^{2} + 72 \, b^{3}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left({\left(-48 i \, a^{2} b + 48 \, a b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(-36 i \, a^{2} b + 36 \, a b^{2}\right)} c^{2} + {\left(-36 i \, a b^{2} + 36 \, b^{3} + {\left(72 i \, a^{2} b - 72 \, a b^{2}\right)} c\right)} {\left(d \sqrt{x} + c\right)} + {\left(36 i \, a b^{2} - 36 \, b^{3}\right)} c + {\left({\left(-48 i \, a^{2} b - 48 \, a b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left(-36 i \, a^{2} b - 36 \, a b^{2}\right)} c^{2} + {\left(-36 i \, a b^{2} - 36 \, b^{3} + {\left(72 i \, a^{2} b + 72 \, a b^{2}\right)} c\right)} {\left(d \sqrt{x} + c\right)} + {\left(36 i \, a b^{2} + 36 \, b^{3}\right)} c\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 12 \, {\left(4 \, {\left(a^{2} b - i \, a b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{2} + 3 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{2} + 3 \, {\left(a b^{2} - i \, b^{3} - 2 \, {\left(a^{2} b - i \, a b^{2}\right)} c\right)} {\left(d \sqrt{x} + c\right)} - 3 \, {\left(a b^{2} - i \, b^{3}\right)} c\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_2\left(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}}{-i \, a + b}\right) + {\left(18 \, {\left(a b^{2} - i \, b^{3}\right)} c^{2} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(18 i \, a b^{2} + 18 \, b^{3}\right)} c^{2} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + 18 \, {\left(a b^{2} + i \, b^{3}\right)} c^{2}\right)} \log\left({\left(a^{2} + b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 4 \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right)\right) + {\left(16 \, {\left(a^{2} b + i \, a b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + 18 \, {\left(a b^{2} + i \, b^{3} - 2 \, {\left(a^{2} b + i \, a b^{2}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{2} + 36 \, {\left({\left(a^{2} b + i \, a b^{2}\right)} c^{2} - {\left(a b^{2} + i \, b^{3}\right)} c\right)} {\left(d \sqrt{x} + c\right)} + 2 \, {\left(8 \, {\left(a^{2} b - i \, a b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + 9 \, {\left(a b^{2} - i \, b^{3} - 2 \, {\left(a^{2} b - i \, a b^{2}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{2} + 18 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} c^{2} - {\left(a b^{2} - i \, b^{3}\right)} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left({\left(16 i \, a^{2} b + 16 \, a b^{2}\right)} {\left(d \sqrt{x} + c\right)}^{3} + {\left(18 i \, a b^{2} + 18 \, b^{3} + {\left(-36 i \, a^{2} b - 36 \, a b^{2}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{2} + {\left({\left(36 i \, a^{2} b + 36 \, a b^{2}\right)} c^{2} + {\left(-36 i \, a b^{2} - 36 \, b^{3}\right)} c\right)} {\left(d \sqrt{x} + c\right)}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \log\left(\frac{{\left(a^{2} + b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 4 \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right)}{a^{2} + b^{2}}\right) + {\left(24 i \, a^{2} b - 24 \, a b^{2} + {\left(24 i \, a^{2} b + 24 \, a b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 24 \, {\left(a^{2} b - i \, a b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{4}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}}{-i \, a + b}) + {\left(18 \, a b^{2} + 18 i \, b^{3} + 48 \, {\left(a^{2} b + i \, a b^{2}\right)} {\left(d \sqrt{x} + c\right)} - 36 \, {\left(a^{2} b + i \, a b^{2}\right)} c + {\left(18 \, a b^{2} - 18 i \, b^{3} + 48 \, {\left(a^{2} b - i \, a b^{2}\right)} {\left(d \sqrt{x} + c\right)} - 36 \, {\left(a^{2} b - i \, a b^{2}\right)} c\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(18 i \, a b^{2} + 18 \, b^{3} + {\left(48 i \, a^{2} b + 48 \, a b^{2}\right)} {\left(d \sqrt{x} + c\right)} + {\left(-36 i \, a^{2} b - 36 \, a b^{2}\right)} c\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{3}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}}{-i \, a + b}) + {\left({\left(3 i \, a^{3} + 9 \, a^{2} b - 9 i \, a b^{2} - 3 \, b^{3}\right)} {\left(d \sqrt{x} + c\right)}^{4} + {\left(24 \, a b^{2} - 24 i \, b^{3} + {\left(-12 i \, a^{3} - 36 \, a^{2} b + 36 i \, a b^{2} + 12 \, b^{3}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{3} + 72 \, {\left(a b^{2} - i \, b^{3}\right)} {\left(d \sqrt{x} + c\right)} c^{2} + {\left({\left(18 i \, a^{3} + 54 \, a^{2} b - 54 i \, a b^{2} - 18 \, b^{3}\right)} c^{2} - 72 \, {\left(a b^{2} - i \, b^{3}\right)} c\right)} {\left(d \sqrt{x} + c\right)}^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)}{12 \, a^{5} + 12 i \, a^{4} b + 24 \, a^{3} b^{2} + 24 i \, a^{2} b^{3} + 12 \, a b^{4} + 12 i \, b^{5} + {\left(12 \, a^{5} - 12 i \, a^{4} b + 24 \, a^{3} b^{2} - 24 i \, a^{2} b^{3} + 12 \, a b^{4} - 12 i \, b^{5}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(12 i \, a^{5} + 12 \, a^{4} b + 24 i \, a^{3} b^{2} + 24 \, a^{2} b^{3} + 12 i \, a b^{4} + 12 \, b^{5}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)}\right)}}{d^{4}}"," ",0,"-2*((2*a*b*log(b*tan(d*sqrt(x) + c) + a)/(a^4 + 2*a^2*b^2 + b^4) - a*b*log(tan(d*sqrt(x) + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + (a^2 - b^2)*(d*sqrt(x) + c)/(a^4 + 2*a^2*b^2 + b^4) - b/(a^3 + a*b^2 + (a^2*b + b^3)*tan(d*sqrt(x) + c)))*c^3 - ((3*a^3 - 3*I*a^2*b + 3*a*b^2 - 3*I*b^3)*(d*sqrt(x) + c)^4 - (12*a^3 - 12*I*a^2*b + 12*a*b^2 - 12*I*b^3)*(d*sqrt(x) + c)^3*c + (18*a^3 - 18*I*a^2*b + 18*a*b^2 - 18*I*b^3)*(d*sqrt(x) + c)^2*c^2 + ((36*I*a*b^2 + 36*b^3)*c^2*cos(2*d*sqrt(x) + 2*c) - 36*(a*b^2 - I*b^3)*c^2*sin(2*d*sqrt(x) + 2*c) + (36*I*a*b^2 - 36*b^3)*c^2)*arctan2(-b*cos(2*d*sqrt(x) + 2*c) + a*sin(2*d*sqrt(x) + 2*c) + b, a*cos(2*d*sqrt(x) + 2*c) + b*sin(2*d*sqrt(x) + 2*c) + a) + ((-32*I*a^2*b + 32*a*b^2)*(d*sqrt(x) + c)^3 + (-36*I*a*b^2 + 36*b^3 + (72*I*a^2*b - 72*a*b^2)*c)*(d*sqrt(x) + c)^2 + ((-72*I*a^2*b + 72*a*b^2)*c^2 + (72*I*a*b^2 - 72*b^3)*c)*(d*sqrt(x) + c) + ((-32*I*a^2*b - 32*a*b^2)*(d*sqrt(x) + c)^3 + (-36*I*a*b^2 - 36*b^3 + (72*I*a^2*b + 72*a*b^2)*c)*(d*sqrt(x) + c)^2 + ((-72*I*a^2*b - 72*a*b^2)*c^2 + (72*I*a*b^2 + 72*b^3)*c)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) + 4*(8*(a^2*b - I*a*b^2)*(d*sqrt(x) + c)^3 + 9*(a*b^2 - I*b^3 - 2*(a^2*b - I*a*b^2)*c)*(d*sqrt(x) + c)^2 + 18*((a^2*b - I*a*b^2)*c^2 - (a*b^2 - I*b^3)*c)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*arctan2((2*a*b*cos(2*d*sqrt(x) + 2*c) - (a^2 - b^2)*sin(2*d*sqrt(x) + 2*c))/(a^2 + b^2), (2*a*b*sin(2*d*sqrt(x) + 2*c) + a^2 + b^2 + (a^2 - b^2)*cos(2*d*sqrt(x) + 2*c))/(a^2 + b^2)) + ((3*a^3 - 9*I*a^2*b - 9*a*b^2 + 3*I*b^3)*(d*sqrt(x) + c)^4 + (-24*I*a*b^2 - 24*b^3 - (12*a^3 - 36*I*a^2*b - 36*a*b^2 + 12*I*b^3)*c)*(d*sqrt(x) + c)^3 + (-72*I*a*b^2 - 72*b^3)*(d*sqrt(x) + c)*c^2 + ((18*a^3 - 54*I*a^2*b - 54*a*b^2 + 18*I*b^3)*c^2 + (72*I*a*b^2 + 72*b^3)*c)*(d*sqrt(x) + c)^2)*cos(2*d*sqrt(x) + 2*c) + ((-48*I*a^2*b + 48*a*b^2)*(d*sqrt(x) + c)^2 + (-36*I*a^2*b + 36*a*b^2)*c^2 + (-36*I*a*b^2 + 36*b^3 + (72*I*a^2*b - 72*a*b^2)*c)*(d*sqrt(x) + c) + (36*I*a*b^2 - 36*b^3)*c + ((-48*I*a^2*b - 48*a*b^2)*(d*sqrt(x) + c)^2 + (-36*I*a^2*b - 36*a*b^2)*c^2 + (-36*I*a*b^2 - 36*b^3 + (72*I*a^2*b + 72*a*b^2)*c)*(d*sqrt(x) + c) + (36*I*a*b^2 + 36*b^3)*c)*cos(2*d*sqrt(x) + 2*c) + 12*(4*(a^2*b - I*a*b^2)*(d*sqrt(x) + c)^2 + 3*(a^2*b - I*a*b^2)*c^2 + 3*(a*b^2 - I*b^3 - 2*(a^2*b - I*a*b^2)*c)*(d*sqrt(x) + c) - 3*(a*b^2 - I*b^3)*c)*sin(2*d*sqrt(x) + 2*c))*dilog((I*a + b)*e^(2*I*d*sqrt(x) + 2*I*c)/(-I*a + b)) + (18*(a*b^2 - I*b^3)*c^2*cos(2*d*sqrt(x) + 2*c) + (18*I*a*b^2 + 18*b^3)*c^2*sin(2*d*sqrt(x) + 2*c) + 18*(a*b^2 + I*b^3)*c^2)*log((a^2 + b^2)*cos(2*d*sqrt(x) + 2*c)^2 + 4*a*b*sin(2*d*sqrt(x) + 2*c) + (a^2 + b^2)*sin(2*d*sqrt(x) + 2*c)^2 + a^2 + b^2 + 2*(a^2 - b^2)*cos(2*d*sqrt(x) + 2*c)) + (16*(a^2*b + I*a*b^2)*(d*sqrt(x) + c)^3 + 18*(a*b^2 + I*b^3 - 2*(a^2*b + I*a*b^2)*c)*(d*sqrt(x) + c)^2 + 36*((a^2*b + I*a*b^2)*c^2 - (a*b^2 + I*b^3)*c)*(d*sqrt(x) + c) + 2*(8*(a^2*b - I*a*b^2)*(d*sqrt(x) + c)^3 + 9*(a*b^2 - I*b^3 - 2*(a^2*b - I*a*b^2)*c)*(d*sqrt(x) + c)^2 + 18*((a^2*b - I*a*b^2)*c^2 - (a*b^2 - I*b^3)*c)*(d*sqrt(x) + c))*cos(2*d*sqrt(x) + 2*c) + ((16*I*a^2*b + 16*a*b^2)*(d*sqrt(x) + c)^3 + (18*I*a*b^2 + 18*b^3 + (-36*I*a^2*b - 36*a*b^2)*c)*(d*sqrt(x) + c)^2 + ((36*I*a^2*b + 36*a*b^2)*c^2 + (-36*I*a*b^2 - 36*b^3)*c)*(d*sqrt(x) + c))*sin(2*d*sqrt(x) + 2*c))*log(((a^2 + b^2)*cos(2*d*sqrt(x) + 2*c)^2 + 4*a*b*sin(2*d*sqrt(x) + 2*c) + (a^2 + b^2)*sin(2*d*sqrt(x) + 2*c)^2 + a^2 + b^2 + 2*(a^2 - b^2)*cos(2*d*sqrt(x) + 2*c))/(a^2 + b^2)) + (24*I*a^2*b - 24*a*b^2 + (24*I*a^2*b + 24*a*b^2)*cos(2*d*sqrt(x) + 2*c) - 24*(a^2*b - I*a*b^2)*sin(2*d*sqrt(x) + 2*c))*polylog(4, (I*a + b)*e^(2*I*d*sqrt(x) + 2*I*c)/(-I*a + b)) + (18*a*b^2 + 18*I*b^3 + 48*(a^2*b + I*a*b^2)*(d*sqrt(x) + c) - 36*(a^2*b + I*a*b^2)*c + (18*a*b^2 - 18*I*b^3 + 48*(a^2*b - I*a*b^2)*(d*sqrt(x) + c) - 36*(a^2*b - I*a*b^2)*c)*cos(2*d*sqrt(x) + 2*c) + (18*I*a*b^2 + 18*b^3 + (48*I*a^2*b + 48*a*b^2)*(d*sqrt(x) + c) + (-36*I*a^2*b - 36*a*b^2)*c)*sin(2*d*sqrt(x) + 2*c))*polylog(3, (I*a + b)*e^(2*I*d*sqrt(x) + 2*I*c)/(-I*a + b)) + ((3*I*a^3 + 9*a^2*b - 9*I*a*b^2 - 3*b^3)*(d*sqrt(x) + c)^4 + (24*a*b^2 - 24*I*b^3 + (-12*I*a^3 - 36*a^2*b + 36*I*a*b^2 + 12*b^3)*c)*(d*sqrt(x) + c)^3 + 72*(a*b^2 - I*b^3)*(d*sqrt(x) + c)*c^2 + ((18*I*a^3 + 54*a^2*b - 54*I*a*b^2 - 18*b^3)*c^2 - 72*(a*b^2 - I*b^3)*c)*(d*sqrt(x) + c)^2)*sin(2*d*sqrt(x) + 2*c))/(12*a^5 + 12*I*a^4*b + 24*a^3*b^2 + 24*I*a^2*b^3 + 12*a*b^4 + 12*I*b^5 + (12*a^5 - 12*I*a^4*b + 24*a^3*b^2 - 24*I*a^2*b^3 + 12*a*b^4 - 12*I*b^5)*cos(2*d*sqrt(x) + 2*c) + (12*I*a^5 + 12*a^4*b + 24*I*a^3*b^2 + 24*a^2*b^3 + 12*I*a*b^4 + 12*b^5)*sin(2*d*sqrt(x) + 2*c)))/d^4","B",0
44,1,1003,0,1.438963," ","integrate(1/(a+b*tan(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","\frac{2 \, {\left({\left(a^{3} - i \, a^{2} b + a b^{2} - i \, b^{3}\right)} d^{2} x + {\left(2 i \, a b^{2} - 2 \, b^{3} + {\left(2 i \, a b^{2} + 2 \, b^{3}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 2 \, {\left(a b^{2} - i \, b^{3}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \arctan\left(-b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + a \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + b, a \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + a\right) + {\left({\left(-4 i \, a^{2} b - 4 \, a b^{2}\right)} d \sqrt{x} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 4 \, {\left(a^{2} b - i \, a b^{2}\right)} d \sqrt{x} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(-4 i \, a^{2} b + 4 \, a b^{2}\right)} d \sqrt{x}\right)} \arctan\left(\frac{2 \, a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(a^{2} - b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)}{a^{2} + b^{2}}, \frac{2 \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + a^{2} + b^{2} + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right)}{a^{2} + b^{2}}\right) + {\left({\left(a^{3} - 3 i \, a^{2} b - 3 \, a b^{2} + i \, b^{3}\right)} d^{2} x + {\left(-4 i \, a b^{2} - 4 \, b^{3}\right)} d \sqrt{x}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(-2 i \, a^{2} b + 2 \, a b^{2} + {\left(-2 i \, a^{2} b - 2 \, a b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 2 \, {\left(a^{2} b - i \, a b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_2\left(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}}{-i \, a + b}\right) + {\left(a b^{2} + i \, b^{3} + {\left(a b^{2} - i \, b^{3}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(i \, a b^{2} + b^{3}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \log\left({\left(a^{2} + b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 4 \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right)\right) + {\left(2 \, {\left(a^{2} b - i \, a b^{2}\right)} d \sqrt{x} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(2 i \, a^{2} b + 2 \, a b^{2}\right)} d \sqrt{x} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + 2 \, {\left(a^{2} b + i \, a b^{2}\right)} d \sqrt{x}\right)} \log\left(\frac{{\left(a^{2} + b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 4 \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right)}{a^{2} + b^{2}}\right) + {\left({\left(i \, a^{3} + 3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} d^{2} x + 4 \, {\left(a b^{2} - i \, b^{3}\right)} d \sqrt{x}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)}}{{\left(2 \, a^{5} - 2 i \, a^{4} b + 4 \, a^{3} b^{2} - 4 i \, a^{2} b^{3} + 2 \, a b^{4} - 2 i \, b^{5}\right)} d^{2} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(2 i \, a^{5} + 2 \, a^{4} b + 4 i \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 2 i \, a b^{4} + 2 \, b^{5}\right)} d^{2} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(2 \, a^{5} + 2 i \, a^{4} b + 4 \, a^{3} b^{2} + 4 i \, a^{2} b^{3} + 2 \, a b^{4} + 2 i \, b^{5}\right)} d^{2}}"," ",0,"2*((a^3 - I*a^2*b + a*b^2 - I*b^3)*d^2*x + (2*I*a*b^2 - 2*b^3 + (2*I*a*b^2 + 2*b^3)*cos(2*d*sqrt(x) + 2*c) - 2*(a*b^2 - I*b^3)*sin(2*d*sqrt(x) + 2*c))*arctan2(-b*cos(2*d*sqrt(x) + 2*c) + a*sin(2*d*sqrt(x) + 2*c) + b, a*cos(2*d*sqrt(x) + 2*c) + b*sin(2*d*sqrt(x) + 2*c) + a) + ((-4*I*a^2*b - 4*a*b^2)*d*sqrt(x)*cos(2*d*sqrt(x) + 2*c) + 4*(a^2*b - I*a*b^2)*d*sqrt(x)*sin(2*d*sqrt(x) + 2*c) + (-4*I*a^2*b + 4*a*b^2)*d*sqrt(x))*arctan2((2*a*b*cos(2*d*sqrt(x) + 2*c) - (a^2 - b^2)*sin(2*d*sqrt(x) + 2*c))/(a^2 + b^2), (2*a*b*sin(2*d*sqrt(x) + 2*c) + a^2 + b^2 + (a^2 - b^2)*cos(2*d*sqrt(x) + 2*c))/(a^2 + b^2)) + ((a^3 - 3*I*a^2*b - 3*a*b^2 + I*b^3)*d^2*x + (-4*I*a*b^2 - 4*b^3)*d*sqrt(x))*cos(2*d*sqrt(x) + 2*c) + (-2*I*a^2*b + 2*a*b^2 + (-2*I*a^2*b - 2*a*b^2)*cos(2*d*sqrt(x) + 2*c) + 2*(a^2*b - I*a*b^2)*sin(2*d*sqrt(x) + 2*c))*dilog((I*a + b)*e^(2*I*d*sqrt(x) + 2*I*c)/(-I*a + b)) + (a*b^2 + I*b^3 + (a*b^2 - I*b^3)*cos(2*d*sqrt(x) + 2*c) + (I*a*b^2 + b^3)*sin(2*d*sqrt(x) + 2*c))*log((a^2 + b^2)*cos(2*d*sqrt(x) + 2*c)^2 + 4*a*b*sin(2*d*sqrt(x) + 2*c) + (a^2 + b^2)*sin(2*d*sqrt(x) + 2*c)^2 + a^2 + b^2 + 2*(a^2 - b^2)*cos(2*d*sqrt(x) + 2*c)) + (2*(a^2*b - I*a*b^2)*d*sqrt(x)*cos(2*d*sqrt(x) + 2*c) + (2*I*a^2*b + 2*a*b^2)*d*sqrt(x)*sin(2*d*sqrt(x) + 2*c) + 2*(a^2*b + I*a*b^2)*d*sqrt(x))*log(((a^2 + b^2)*cos(2*d*sqrt(x) + 2*c)^2 + 4*a*b*sin(2*d*sqrt(x) + 2*c) + (a^2 + b^2)*sin(2*d*sqrt(x) + 2*c)^2 + a^2 + b^2 + 2*(a^2 - b^2)*cos(2*d*sqrt(x) + 2*c))/(a^2 + b^2)) + ((I*a^3 + 3*a^2*b - 3*I*a*b^2 - b^3)*d^2*x + 4*(a*b^2 - I*b^3)*d*sqrt(x))*sin(2*d*sqrt(x) + 2*c))/((2*a^5 - 2*I*a^4*b + 4*a^3*b^2 - 4*I*a^2*b^3 + 2*a*b^4 - 2*I*b^5)*d^2*cos(2*d*sqrt(x) + 2*c) + (2*I*a^5 + 2*a^4*b + 4*I*a^3*b^2 + 4*a^2*b^3 + 2*I*a*b^4 + 2*b^5)*d^2*sin(2*d*sqrt(x) + 2*c) + (2*a^5 + 2*I*a^4*b + 4*a^3*b^2 + 4*I*a^2*b^3 + 2*a*b^4 + 2*I*b^5)*d^2)","B",0
45,0,0,0,0.000000," ","integrate(1/x/(a+b*tan(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","\frac{-2 \, {\left({\left({\left(4 \, a^{10} b^{2} + 16 \, a^{8} b^{4} + 24 \, a^{6} b^{6} + 17 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} \cos\left(2 \, c\right)^{2} + {\left(4 \, a^{10} b^{2} + 16 \, a^{8} b^{4} + 24 \, a^{6} b^{6} + 17 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} \sin\left(2 \, c\right)^{2}\right)} d \cos\left(2 \, d \sqrt{x}\right)^{2} + {\left(a^{12} + 2 \, a^{10} b^{2} + a^{8} b^{4}\right)} d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + {\left({\left(4 \, a^{10} b^{2} + 16 \, a^{8} b^{4} + 24 \, a^{6} b^{6} + 17 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} \cos\left(2 \, c\right)^{2} + {\left(4 \, a^{10} b^{2} + 16 \, a^{8} b^{4} + 24 \, a^{6} b^{6} + 17 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} \sin\left(2 \, c\right)^{2}\right)} d \sin\left(2 \, d \sqrt{x}\right)^{2} + {\left(a^{12} + 2 \, a^{10} b^{2} + a^{8} b^{4}\right)} d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} - 2 \, {\left({\left(a^{8} b^{4} + 4 \, a^{6} b^{6} + 6 \, a^{4} b^{8} + 4 \, a^{2} b^{10} + b^{12}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{11} b + 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} + 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} + a b^{11}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d \sqrt{x}\right) + 2 \, {\left(2 \, {\left(a^{11} b + 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} + 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} + a b^{11}\right)} \cos\left(2 \, c\right) + {\left(a^{8} b^{4} + 4 \, a^{6} b^{6} + 6 \, a^{4} b^{8} + 4 \, a^{2} b^{10} + b^{12}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d \sqrt{x}\right) + {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d - 2 \, {\left({\left({\left(a^{8} b^{4} + 2 \, a^{6} b^{6} + a^{4} b^{8}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d \sqrt{x}\right) - {\left(2 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} \cos\left(2 \, c\right) + {\left(a^{8} b^{4} + 2 \, a^{6} b^{6} + a^{4} b^{8}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d \sqrt{x}\right) - {\left(a^{12} + 4 \, a^{10} b^{2} + 6 \, a^{8} b^{4} + 4 \, a^{6} b^{6} + a^{4} b^{8}\right)} d\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 2 \, {\left({\left(2 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} \cos\left(2 \, c\right) + {\left(a^{8} b^{4} + 2 \, a^{6} b^{6} + a^{4} b^{8}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d \sqrt{x}\right) + {\left({\left(a^{8} b^{4} + 2 \, a^{6} b^{6} + a^{4} b^{8}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d \sqrt{x}\right)\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} x \int \frac{2 \, {\left(a^{5} b d \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(a b^{5} \sin\left(2 \, c\right) + 2 \, {\left(a^{4} b^{2} + a^{2} b^{4}\right)} \cos\left(2 \, c\right)\right)} d \cos\left(2 \, d \sqrt{x}\right) - {\left(a b^{5} \cos\left(2 \, c\right) - 2 \, {\left(a^{4} b^{2} + a^{2} b^{4}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d \sqrt{x}\right)\right)} x - {\left(a^{4} b^{2} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(b^{6} \sin\left(2 \, c\right) + 2 \, {\left(a^{3} b^{3} + a b^{5}\right)} \cos\left(2 \, c\right)\right)} \cos\left(2 \, d \sqrt{x}\right) - {\left(b^{6} \cos\left(2 \, c\right) - 2 \, {\left(a^{3} b^{3} + a b^{5}\right)} \sin\left(2 \, c\right)\right)} \sin\left(2 \, d \sqrt{x}\right)\right)} \sqrt{x}}{{\left(a^{8} d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + a^{8} d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + {\left({\left(4 \, a^{6} b^{2} + 8 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} \cos\left(2 \, c\right)^{2} + {\left(4 \, a^{6} b^{2} + 8 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} \sin\left(2 \, c\right)^{2}\right)} d \cos\left(2 \, d \sqrt{x}\right)^{2} + {\left({\left(4 \, a^{6} b^{2} + 8 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} \cos\left(2 \, c\right)^{2} + {\left(4 \, a^{6} b^{2} + 8 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} \sin\left(2 \, c\right)^{2}\right)} d \sin\left(2 \, d \sqrt{x}\right)^{2} - 2 \, {\left({\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d \sqrt{x}\right) + 2 \, {\left(2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} \cos\left(2 \, c\right) + {\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d \sqrt{x}\right) + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d - 2 \, {\left({\left(a^{4} b^{4} \cos\left(2 \, c\right) - 2 \, {\left(a^{7} b + a^{5} b^{3}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d \sqrt{x}\right) - {\left(a^{4} b^{4} \sin\left(2 \, c\right) + 2 \, {\left(a^{7} b + a^{5} b^{3}\right)} \cos\left(2 \, c\right)\right)} d \sin\left(2 \, d \sqrt{x}\right) - {\left(a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} d\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 2 \, {\left({\left(a^{4} b^{4} \sin\left(2 \, c\right) + 2 \, {\left(a^{7} b + a^{5} b^{3}\right)} \cos\left(2 \, c\right)\right)} d \cos\left(2 \, d \sqrt{x}\right) + {\left(a^{4} b^{4} \cos\left(2 \, c\right) - 2 \, {\left(a^{7} b + a^{5} b^{3}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d \sqrt{x}\right)\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} x^{2}}\,{d x} + {\left({\left({\left(4 \, a^{8} b^{2} + 4 \, a^{6} b^{4} - 4 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} \cos\left(2 \, c\right)^{2} + {\left(4 \, a^{8} b^{2} + 4 \, a^{6} b^{4} - 4 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} \sin\left(2 \, c\right)^{2}\right)} d \cos\left(2 \, d \sqrt{x}\right)^{2} + {\left(a^{10} - a^{8} b^{2}\right)} d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + {\left({\left(4 \, a^{8} b^{2} + 4 \, a^{6} b^{4} - 4 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} \cos\left(2 \, c\right)^{2} + {\left(4 \, a^{8} b^{2} + 4 \, a^{6} b^{4} - 4 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} \sin\left(2 \, c\right)^{2}\right)} d \sin\left(2 \, d \sqrt{x}\right)^{2} + {\left(a^{10} - a^{8} b^{2}\right)} d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} - 2 \, {\left({\left(a^{6} b^{4} + a^{4} b^{6} - a^{2} b^{8} - b^{10}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{9} b + 2 \, a^{7} b^{3} - 2 \, a^{3} b^{7} - a b^{9}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d \sqrt{x}\right) + 2 \, {\left(2 \, {\left(a^{9} b + 2 \, a^{7} b^{3} - 2 \, a^{3} b^{7} - a b^{9}\right)} \cos\left(2 \, c\right) + {\left(a^{6} b^{4} + a^{4} b^{6} - a^{2} b^{8} - b^{10}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d \sqrt{x}\right) + {\left(a^{10} + 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} d - 2 \, {\left({\left({\left(a^{6} b^{4} - a^{4} b^{6}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{9} b - a^{5} b^{5}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d \sqrt{x}\right) - {\left(2 \, {\left(a^{9} b - a^{5} b^{5}\right)} \cos\left(2 \, c\right) + {\left(a^{6} b^{4} - a^{4} b^{6}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d \sqrt{x}\right) - {\left(a^{10} + a^{8} b^{2} - a^{6} b^{4} - a^{4} b^{6}\right)} d\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 2 \, {\left({\left(2 \, {\left(a^{9} b - a^{5} b^{5}\right)} \cos\left(2 \, c\right) + {\left(a^{6} b^{4} - a^{4} b^{6}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d \sqrt{x}\right) + {\left({\left(a^{6} b^{4} - a^{4} b^{6}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{9} b - a^{5} b^{5}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d \sqrt{x}\right)\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} x \log\left(x\right) - 4 \, {\left({\left(2 \, {\left(a^{7} b^{3} + 3 \, a^{5} b^{5} + 3 \, a^{3} b^{7} + a b^{9}\right)} \cos\left(2 \, c\right) + {\left(a^{4} b^{6} + 2 \, a^{2} b^{8} + b^{10}\right)} \sin\left(2 \, c\right)\right)} \cos\left(2 \, d \sqrt{x}\right) + {\left({\left(a^{4} b^{6} + 2 \, a^{2} b^{8} + b^{10}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{7} b^{3} + 3 \, a^{5} b^{5} + 3 \, a^{3} b^{7} + a b^{9}\right)} \sin\left(2 \, c\right)\right)} \sin\left(2 \, d \sqrt{x}\right) - {\left(a^{8} b^{2} + 2 \, a^{6} b^{4} + a^{4} b^{6}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \sqrt{x}}{{\left({\left({\left(4 \, a^{10} b^{2} + 16 \, a^{8} b^{4} + 24 \, a^{6} b^{6} + 17 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} \cos\left(2 \, c\right)^{2} + {\left(4 \, a^{10} b^{2} + 16 \, a^{8} b^{4} + 24 \, a^{6} b^{6} + 17 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} \sin\left(2 \, c\right)^{2}\right)} d \cos\left(2 \, d \sqrt{x}\right)^{2} + {\left(a^{12} + 2 \, a^{10} b^{2} + a^{8} b^{4}\right)} d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + {\left({\left(4 \, a^{10} b^{2} + 16 \, a^{8} b^{4} + 24 \, a^{6} b^{6} + 17 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} \cos\left(2 \, c\right)^{2} + {\left(4 \, a^{10} b^{2} + 16 \, a^{8} b^{4} + 24 \, a^{6} b^{6} + 17 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} \sin\left(2 \, c\right)^{2}\right)} d \sin\left(2 \, d \sqrt{x}\right)^{2} + {\left(a^{12} + 2 \, a^{10} b^{2} + a^{8} b^{4}\right)} d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} - 2 \, {\left({\left(a^{8} b^{4} + 4 \, a^{6} b^{6} + 6 \, a^{4} b^{8} + 4 \, a^{2} b^{10} + b^{12}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{11} b + 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} + 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} + a b^{11}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d \sqrt{x}\right) + 2 \, {\left(2 \, {\left(a^{11} b + 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} + 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} + a b^{11}\right)} \cos\left(2 \, c\right) + {\left(a^{8} b^{4} + 4 \, a^{6} b^{6} + 6 \, a^{4} b^{8} + 4 \, a^{2} b^{10} + b^{12}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d \sqrt{x}\right) + {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d - 2 \, {\left({\left({\left(a^{8} b^{4} + 2 \, a^{6} b^{6} + a^{4} b^{8}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d \sqrt{x}\right) - {\left(2 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} \cos\left(2 \, c\right) + {\left(a^{8} b^{4} + 2 \, a^{6} b^{6} + a^{4} b^{8}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d \sqrt{x}\right) - {\left(a^{12} + 4 \, a^{10} b^{2} + 6 \, a^{8} b^{4} + 4 \, a^{6} b^{6} + a^{4} b^{8}\right)} d\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 2 \, {\left({\left(2 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} \cos\left(2 \, c\right) + {\left(a^{8} b^{4} + 2 \, a^{6} b^{6} + a^{4} b^{8}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d \sqrt{x}\right) + {\left({\left(a^{8} b^{4} + 2 \, a^{6} b^{6} + a^{4} b^{8}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d \sqrt{x}\right)\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} x}"," ",0,"((((4*a^10*b^2 + 16*a^8*b^4 + 24*a^6*b^6 + 17*a^4*b^8 + 6*a^2*b^10 + b^12)*cos(2*c)^2 + (4*a^10*b^2 + 16*a^8*b^4 + 24*a^6*b^6 + 17*a^4*b^8 + 6*a^2*b^10 + b^12)*sin(2*c)^2)*d*cos(2*d*sqrt(x))^2 + (a^12 + 2*a^10*b^2 + a^8*b^4)*d*cos(2*d*sqrt(x) + 2*c)^2 + ((4*a^10*b^2 + 16*a^8*b^4 + 24*a^6*b^6 + 17*a^4*b^8 + 6*a^2*b^10 + b^12)*cos(2*c)^2 + (4*a^10*b^2 + 16*a^8*b^4 + 24*a^6*b^6 + 17*a^4*b^8 + 6*a^2*b^10 + b^12)*sin(2*c)^2)*d*sin(2*d*sqrt(x))^2 + (a^12 + 2*a^10*b^2 + a^8*b^4)*d*sin(2*d*sqrt(x) + 2*c)^2 - 2*((a^8*b^4 + 4*a^6*b^6 + 6*a^4*b^8 + 4*a^2*b^10 + b^12)*cos(2*c) - 2*(a^11*b + 5*a^9*b^3 + 10*a^7*b^5 + 10*a^5*b^7 + 5*a^3*b^9 + a*b^11)*sin(2*c))*d*cos(2*d*sqrt(x)) + 2*(2*(a^11*b + 5*a^9*b^3 + 10*a^7*b^5 + 10*a^5*b^7 + 5*a^3*b^9 + a*b^11)*cos(2*c) + (a^8*b^4 + 4*a^6*b^6 + 6*a^4*b^8 + 4*a^2*b^10 + b^12)*sin(2*c))*d*sin(2*d*sqrt(x)) + (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d - 2*(((a^8*b^4 + 2*a^6*b^6 + a^4*b^8)*cos(2*c) - 2*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*sin(2*c))*d*cos(2*d*sqrt(x)) - (2*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*cos(2*c) + (a^8*b^4 + 2*a^6*b^6 + a^4*b^8)*sin(2*c))*d*sin(2*d*sqrt(x)) - (a^12 + 4*a^10*b^2 + 6*a^8*b^4 + 4*a^6*b^6 + a^4*b^8)*d)*cos(2*d*sqrt(x) + 2*c) - 2*((2*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*cos(2*c) + (a^8*b^4 + 2*a^6*b^6 + a^4*b^8)*sin(2*c))*d*cos(2*d*sqrt(x)) + ((a^8*b^4 + 2*a^6*b^6 + a^4*b^8)*cos(2*c) - 2*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*sin(2*c))*d*sin(2*d*sqrt(x)))*sin(2*d*sqrt(x) + 2*c))*x*integrate(-2*(2*(a^5*b*d*sin(2*d*sqrt(x) + 2*c) - (a*b^5*sin(2*c) + 2*(a^4*b^2 + a^2*b^4)*cos(2*c))*d*cos(2*d*sqrt(x)) - (a*b^5*cos(2*c) - 2*(a^4*b^2 + a^2*b^4)*sin(2*c))*d*sin(2*d*sqrt(x)))*x - (a^4*b^2*sin(2*d*sqrt(x) + 2*c) - (b^6*sin(2*c) + 2*(a^3*b^3 + a*b^5)*cos(2*c))*cos(2*d*sqrt(x)) - (b^6*cos(2*c) - 2*(a^3*b^3 + a*b^5)*sin(2*c))*sin(2*d*sqrt(x)))*sqrt(x))/((a^8*d*cos(2*d*sqrt(x) + 2*c)^2 + a^8*d*sin(2*d*sqrt(x) + 2*c)^2 + ((4*a^6*b^2 + 8*a^4*b^4 + 4*a^2*b^6 + b^8)*cos(2*c)^2 + (4*a^6*b^2 + 8*a^4*b^4 + 4*a^2*b^6 + b^8)*sin(2*c)^2)*d*cos(2*d*sqrt(x))^2 + ((4*a^6*b^2 + 8*a^4*b^4 + 4*a^2*b^6 + b^8)*cos(2*c)^2 + (4*a^6*b^2 + 8*a^4*b^4 + 4*a^2*b^6 + b^8)*sin(2*c)^2)*d*sin(2*d*sqrt(x))^2 - 2*((a^4*b^4 + 2*a^2*b^6 + b^8)*cos(2*c) - 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*sin(2*c))*d*cos(2*d*sqrt(x)) + 2*(2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*cos(2*c) + (a^4*b^4 + 2*a^2*b^6 + b^8)*sin(2*c))*d*sin(2*d*sqrt(x)) + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d - 2*((a^4*b^4*cos(2*c) - 2*(a^7*b + a^5*b^3)*sin(2*c))*d*cos(2*d*sqrt(x)) - (a^4*b^4*sin(2*c) + 2*(a^7*b + a^5*b^3)*cos(2*c))*d*sin(2*d*sqrt(x)) - (a^8 + 2*a^6*b^2 + a^4*b^4)*d)*cos(2*d*sqrt(x) + 2*c) - 2*((a^4*b^4*sin(2*c) + 2*(a^7*b + a^5*b^3)*cos(2*c))*d*cos(2*d*sqrt(x)) + (a^4*b^4*cos(2*c) - 2*(a^7*b + a^5*b^3)*sin(2*c))*d*sin(2*d*sqrt(x)))*sin(2*d*sqrt(x) + 2*c))*x^2), x) + (((4*a^8*b^2 + 4*a^6*b^4 - 4*a^4*b^6 - 3*a^2*b^8 - b^10)*cos(2*c)^2 + (4*a^8*b^2 + 4*a^6*b^4 - 4*a^4*b^6 - 3*a^2*b^8 - b^10)*sin(2*c)^2)*d*cos(2*d*sqrt(x))^2 + (a^10 - a^8*b^2)*d*cos(2*d*sqrt(x) + 2*c)^2 + ((4*a^8*b^2 + 4*a^6*b^4 - 4*a^4*b^6 - 3*a^2*b^8 - b^10)*cos(2*c)^2 + (4*a^8*b^2 + 4*a^6*b^4 - 4*a^4*b^6 - 3*a^2*b^8 - b^10)*sin(2*c)^2)*d*sin(2*d*sqrt(x))^2 + (a^10 - a^8*b^2)*d*sin(2*d*sqrt(x) + 2*c)^2 - 2*((a^6*b^4 + a^4*b^6 - a^2*b^8 - b^10)*cos(2*c) - 2*(a^9*b + 2*a^7*b^3 - 2*a^3*b^7 - a*b^9)*sin(2*c))*d*cos(2*d*sqrt(x)) + 2*(2*(a^9*b + 2*a^7*b^3 - 2*a^3*b^7 - a*b^9)*cos(2*c) + (a^6*b^4 + a^4*b^6 - a^2*b^8 - b^10)*sin(2*c))*d*sin(2*d*sqrt(x)) + (a^10 + 3*a^8*b^2 + 2*a^6*b^4 - 2*a^4*b^6 - 3*a^2*b^8 - b^10)*d - 2*(((a^6*b^4 - a^4*b^6)*cos(2*c) - 2*(a^9*b - a^5*b^5)*sin(2*c))*d*cos(2*d*sqrt(x)) - (2*(a^9*b - a^5*b^5)*cos(2*c) + (a^6*b^4 - a^4*b^6)*sin(2*c))*d*sin(2*d*sqrt(x)) - (a^10 + a^8*b^2 - a^6*b^4 - a^4*b^6)*d)*cos(2*d*sqrt(x) + 2*c) - 2*((2*(a^9*b - a^5*b^5)*cos(2*c) + (a^6*b^4 - a^4*b^6)*sin(2*c))*d*cos(2*d*sqrt(x)) + ((a^6*b^4 - a^4*b^6)*cos(2*c) - 2*(a^9*b - a^5*b^5)*sin(2*c))*d*sin(2*d*sqrt(x)))*sin(2*d*sqrt(x) + 2*c))*x*log(x) - 4*((2*(a^7*b^3 + 3*a^5*b^5 + 3*a^3*b^7 + a*b^9)*cos(2*c) + (a^4*b^6 + 2*a^2*b^8 + b^10)*sin(2*c))*cos(2*d*sqrt(x)) + ((a^4*b^6 + 2*a^2*b^8 + b^10)*cos(2*c) - 2*(a^7*b^3 + 3*a^5*b^5 + 3*a^3*b^7 + a*b^9)*sin(2*c))*sin(2*d*sqrt(x)) - (a^8*b^2 + 2*a^6*b^4 + a^4*b^6)*sin(2*d*sqrt(x) + 2*c))*sqrt(x))/((((4*a^10*b^2 + 16*a^8*b^4 + 24*a^6*b^6 + 17*a^4*b^8 + 6*a^2*b^10 + b^12)*cos(2*c)^2 + (4*a^10*b^2 + 16*a^8*b^4 + 24*a^6*b^6 + 17*a^4*b^8 + 6*a^2*b^10 + b^12)*sin(2*c)^2)*d*cos(2*d*sqrt(x))^2 + (a^12 + 2*a^10*b^2 + a^8*b^4)*d*cos(2*d*sqrt(x) + 2*c)^2 + ((4*a^10*b^2 + 16*a^8*b^4 + 24*a^6*b^6 + 17*a^4*b^8 + 6*a^2*b^10 + b^12)*cos(2*c)^2 + (4*a^10*b^2 + 16*a^8*b^4 + 24*a^6*b^6 + 17*a^4*b^8 + 6*a^2*b^10 + b^12)*sin(2*c)^2)*d*sin(2*d*sqrt(x))^2 + (a^12 + 2*a^10*b^2 + a^8*b^4)*d*sin(2*d*sqrt(x) + 2*c)^2 - 2*((a^8*b^4 + 4*a^6*b^6 + 6*a^4*b^8 + 4*a^2*b^10 + b^12)*cos(2*c) - 2*(a^11*b + 5*a^9*b^3 + 10*a^7*b^5 + 10*a^5*b^7 + 5*a^3*b^9 + a*b^11)*sin(2*c))*d*cos(2*d*sqrt(x)) + 2*(2*(a^11*b + 5*a^9*b^3 + 10*a^7*b^5 + 10*a^5*b^7 + 5*a^3*b^9 + a*b^11)*cos(2*c) + (a^8*b^4 + 4*a^6*b^6 + 6*a^4*b^8 + 4*a^2*b^10 + b^12)*sin(2*c))*d*sin(2*d*sqrt(x)) + (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d - 2*(((a^8*b^4 + 2*a^6*b^6 + a^4*b^8)*cos(2*c) - 2*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*sin(2*c))*d*cos(2*d*sqrt(x)) - (2*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*cos(2*c) + (a^8*b^4 + 2*a^6*b^6 + a^4*b^8)*sin(2*c))*d*sin(2*d*sqrt(x)) - (a^12 + 4*a^10*b^2 + 6*a^8*b^4 + 4*a^6*b^6 + a^4*b^8)*d)*cos(2*d*sqrt(x) + 2*c) - 2*((2*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*cos(2*c) + (a^8*b^4 + 2*a^6*b^6 + a^4*b^8)*sin(2*c))*d*cos(2*d*sqrt(x)) + ((a^8*b^4 + 2*a^6*b^6 + a^4*b^8)*cos(2*c) - 2*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*sin(2*c))*d*sin(2*d*sqrt(x)))*sin(2*d*sqrt(x) + 2*c))*x)","F",0
46,-2,0,0,0.000000," ","integrate(1/x^2/(a+b*tan(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
47,1,1119,0,1.159832," ","integrate(x^2*(a+b*tan(c+d*x^(1/3))),x, algorithm=""maxima"")","\frac{35 \, {\left(d x^{\frac{1}{3}} + c\right)}^{9} a + 35 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{9} b - 315 \, {\left(d x^{\frac{1}{3}} + c\right)}^{8} a c - 315 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{8} b c + 1260 \, {\left(d x^{\frac{1}{3}} + c\right)}^{7} a c^{2} + 1260 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{7} b c^{2} - 2940 \, {\left(d x^{\frac{1}{3}} + c\right)}^{6} a c^{3} - 2940 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{6} b c^{3} + 4410 \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} a c^{4} + 4410 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} b c^{4} - 4410 \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} a c^{5} - 4410 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} b c^{5} + 2940 \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} a c^{6} + 2940 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} b c^{6} - 1260 \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} a c^{7} - 1260 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} b c^{7} + 315 \, {\left(d x^{\frac{1}{3}} + c\right)} a c^{8} + 315 \, b c^{8} \log\left(\sec\left(d x^{\frac{1}{3}} + c\right)\right) - {\left(5040 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{8} b - 23040 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{7} b c + 47040 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{6} b c^{2} - 56448 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} b c^{3} + 44100 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} b c^{4} - 23520 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} b c^{5} + 8820 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} b c^{6} - 2520 i \, {\left(d x^{\frac{1}{3}} + c\right)} b c^{7}\right)} \arctan\left(\sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right), \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 1\right) - {\left(-20160 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{7} b + 80640 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{6} b c - 141120 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} b c^{2} + 141120 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} b c^{3} - 88200 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} b c^{4} + 35280 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} b c^{5} - 8820 i \, {\left(d x^{\frac{1}{3}} + c\right)} b c^{6} + 1260 i \, b c^{7}\right)} {\rm Li}_2\left(-e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}\right) - 6 \, {\left(420 \, {\left(d x^{\frac{1}{3}} + c\right)}^{8} b - 1920 \, {\left(d x^{\frac{1}{3}} + c\right)}^{7} b c + 3920 \, {\left(d x^{\frac{1}{3}} + c\right)}^{6} b c^{2} - 4704 \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} b c^{3} + 3675 \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} b c^{4} - 1960 \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} b c^{5} + 735 \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} b c^{6} - 210 \, {\left(d x^{\frac{1}{3}} + c\right)} b c^{7}\right)} \log\left(\cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 1\right) + 793800 \, b {\rm Li}_{9}(-e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}) - {\left(1587600 i \, {\left(d x^{\frac{1}{3}} + c\right)} b - 907200 i \, b c\right)} {\rm Li}_{8}(-e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}) - 75600 \, {\left(21 \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} b - 24 \, {\left(d x^{\frac{1}{3}} + c\right)} b c + 7 \, b c^{2}\right)} {\rm Li}_{7}(-e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}) - {\left(-1058400 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} b + 1814400 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} b c - 1058400 i \, {\left(d x^{\frac{1}{3}} + c\right)} b c^{2} + 211680 i \, b c^{3}\right)} {\rm Li}_{6}(-e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}) + 1890 \, {\left(280 \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} b - 640 \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} b c + 560 \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} b c^{2} - 224 \, {\left(d x^{\frac{1}{3}} + c\right)} b c^{3} + 35 \, b c^{4}\right)} {\rm Li}_{5}(-e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}) - {\left(211680 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} b - 604800 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} b c + 705600 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} b c^{2} - 423360 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} b c^{3} + 132300 i \, {\left(d x^{\frac{1}{3}} + c\right)} b c^{4} - 17640 i \, b c^{5}\right)} {\rm Li}_{4}(-e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}) - 630 \, {\left(112 \, {\left(d x^{\frac{1}{3}} + c\right)}^{6} b - 384 \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} b c + 560 \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} b c^{2} - 448 \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} b c^{3} + 210 \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} b c^{4} - 56 \, {\left(d x^{\frac{1}{3}} + c\right)} b c^{5} + 7 \, b c^{6}\right)} {\rm Li}_{3}(-e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)})}{105 \, d^{9}}"," ",0,"1/105*(35*(d*x^(1/3) + c)^9*a + 35*I*(d*x^(1/3) + c)^9*b - 315*(d*x^(1/3) + c)^8*a*c - 315*I*(d*x^(1/3) + c)^8*b*c + 1260*(d*x^(1/3) + c)^7*a*c^2 + 1260*I*(d*x^(1/3) + c)^7*b*c^2 - 2940*(d*x^(1/3) + c)^6*a*c^3 - 2940*I*(d*x^(1/3) + c)^6*b*c^3 + 4410*(d*x^(1/3) + c)^5*a*c^4 + 4410*I*(d*x^(1/3) + c)^5*b*c^4 - 4410*(d*x^(1/3) + c)^4*a*c^5 - 4410*I*(d*x^(1/3) + c)^4*b*c^5 + 2940*(d*x^(1/3) + c)^3*a*c^6 + 2940*I*(d*x^(1/3) + c)^3*b*c^6 - 1260*(d*x^(1/3) + c)^2*a*c^7 - 1260*I*(d*x^(1/3) + c)^2*b*c^7 + 315*(d*x^(1/3) + c)*a*c^8 + 315*b*c^8*log(sec(d*x^(1/3) + c)) - (5040*I*(d*x^(1/3) + c)^8*b - 23040*I*(d*x^(1/3) + c)^7*b*c + 47040*I*(d*x^(1/3) + c)^6*b*c^2 - 56448*I*(d*x^(1/3) + c)^5*b*c^3 + 44100*I*(d*x^(1/3) + c)^4*b*c^4 - 23520*I*(d*x^(1/3) + c)^3*b*c^5 + 8820*I*(d*x^(1/3) + c)^2*b*c^6 - 2520*I*(d*x^(1/3) + c)*b*c^7)*arctan2(sin(2*d*x^(1/3) + 2*c), cos(2*d*x^(1/3) + 2*c) + 1) - (-20160*I*(d*x^(1/3) + c)^7*b + 80640*I*(d*x^(1/3) + c)^6*b*c - 141120*I*(d*x^(1/3) + c)^5*b*c^2 + 141120*I*(d*x^(1/3) + c)^4*b*c^3 - 88200*I*(d*x^(1/3) + c)^3*b*c^4 + 35280*I*(d*x^(1/3) + c)^2*b*c^5 - 8820*I*(d*x^(1/3) + c)*b*c^6 + 1260*I*b*c^7)*dilog(-e^(2*I*d*x^(1/3) + 2*I*c)) - 6*(420*(d*x^(1/3) + c)^8*b - 1920*(d*x^(1/3) + c)^7*b*c + 3920*(d*x^(1/3) + c)^6*b*c^2 - 4704*(d*x^(1/3) + c)^5*b*c^3 + 3675*(d*x^(1/3) + c)^4*b*c^4 - 1960*(d*x^(1/3) + c)^3*b*c^5 + 735*(d*x^(1/3) + c)^2*b*c^6 - 210*(d*x^(1/3) + c)*b*c^7)*log(cos(2*d*x^(1/3) + 2*c)^2 + sin(2*d*x^(1/3) + 2*c)^2 + 2*cos(2*d*x^(1/3) + 2*c) + 1) + 793800*b*polylog(9, -e^(2*I*d*x^(1/3) + 2*I*c)) - (1587600*I*(d*x^(1/3) + c)*b - 907200*I*b*c)*polylog(8, -e^(2*I*d*x^(1/3) + 2*I*c)) - 75600*(21*(d*x^(1/3) + c)^2*b - 24*(d*x^(1/3) + c)*b*c + 7*b*c^2)*polylog(7, -e^(2*I*d*x^(1/3) + 2*I*c)) - (-1058400*I*(d*x^(1/3) + c)^3*b + 1814400*I*(d*x^(1/3) + c)^2*b*c - 1058400*I*(d*x^(1/3) + c)*b*c^2 + 211680*I*b*c^3)*polylog(6, -e^(2*I*d*x^(1/3) + 2*I*c)) + 1890*(280*(d*x^(1/3) + c)^4*b - 640*(d*x^(1/3) + c)^3*b*c + 560*(d*x^(1/3) + c)^2*b*c^2 - 224*(d*x^(1/3) + c)*b*c^3 + 35*b*c^4)*polylog(5, -e^(2*I*d*x^(1/3) + 2*I*c)) - (211680*I*(d*x^(1/3) + c)^5*b - 604800*I*(d*x^(1/3) + c)^4*b*c + 705600*I*(d*x^(1/3) + c)^3*b*c^2 - 423360*I*(d*x^(1/3) + c)^2*b*c^3 + 132300*I*(d*x^(1/3) + c)*b*c^4 - 17640*I*b*c^5)*polylog(4, -e^(2*I*d*x^(1/3) + 2*I*c)) - 630*(112*(d*x^(1/3) + c)^6*b - 384*(d*x^(1/3) + c)^5*b*c + 560*(d*x^(1/3) + c)^4*b*c^2 - 448*(d*x^(1/3) + c)^3*b*c^3 + 210*(d*x^(1/3) + c)^2*b*c^4 - 56*(d*x^(1/3) + c)*b*c^5 + 7*b*c^6)*polylog(3, -e^(2*I*d*x^(1/3) + 2*I*c)))/d^9","B",0
48,1,618,0,1.230458," ","integrate(x*(a+b*tan(c+d*x^(1/3))),x, algorithm=""maxima"")","\frac{5 \, {\left(d x^{\frac{1}{3}} + c\right)}^{6} a + 5 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{6} b - 30 \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} a c - 30 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} b c + 75 \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} a c^{2} + 75 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} b c^{2} - 100 \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} a c^{3} - 100 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} b c^{3} + 75 \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} a c^{4} + 75 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} b c^{4} - 30 \, {\left(d x^{\frac{1}{3}} + c\right)} a c^{5} - 30 \, b c^{5} \log\left(\sec\left(d x^{\frac{1}{3}} + c\right)\right) - {\left(96 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} b - 300 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} b c + 400 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} b c^{2} - 300 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} b c^{3} + 150 i \, {\left(d x^{\frac{1}{3}} + c\right)} b c^{4}\right)} \arctan\left(\sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right), \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 1\right) - {\left(-240 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} b + 600 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} b c - 600 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} b c^{2} + 300 i \, {\left(d x^{\frac{1}{3}} + c\right)} b c^{3} - 75 i \, b c^{4}\right)} {\rm Li}_2\left(-e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}\right) - {\left(48 \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} b - 150 \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} b c + 200 \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} b c^{2} - 150 \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} b c^{3} + 75 \, {\left(d x^{\frac{1}{3}} + c\right)} b c^{4}\right)} \log\left(\cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 1\right) + 360 i \, b {\rm Li}_{6}(-e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}) + 90 \, {\left(8 \, {\left(d x^{\frac{1}{3}} + c\right)} b - 5 \, b c\right)} {\rm Li}_{5}(-e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}) - {\left(720 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} b - 900 i \, {\left(d x^{\frac{1}{3}} + c\right)} b c + 300 i \, b c^{2}\right)} {\rm Li}_{4}(-e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}) - 30 \, {\left(16 \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} b - 30 \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} b c + 20 \, {\left(d x^{\frac{1}{3}} + c\right)} b c^{2} - 5 \, b c^{3}\right)} {\rm Li}_{3}(-e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)})}{10 \, d^{6}}"," ",0,"1/10*(5*(d*x^(1/3) + c)^6*a + 5*I*(d*x^(1/3) + c)^6*b - 30*(d*x^(1/3) + c)^5*a*c - 30*I*(d*x^(1/3) + c)^5*b*c + 75*(d*x^(1/3) + c)^4*a*c^2 + 75*I*(d*x^(1/3) + c)^4*b*c^2 - 100*(d*x^(1/3) + c)^3*a*c^3 - 100*I*(d*x^(1/3) + c)^3*b*c^3 + 75*(d*x^(1/3) + c)^2*a*c^4 + 75*I*(d*x^(1/3) + c)^2*b*c^4 - 30*(d*x^(1/3) + c)*a*c^5 - 30*b*c^5*log(sec(d*x^(1/3) + c)) - (96*I*(d*x^(1/3) + c)^5*b - 300*I*(d*x^(1/3) + c)^4*b*c + 400*I*(d*x^(1/3) + c)^3*b*c^2 - 300*I*(d*x^(1/3) + c)^2*b*c^3 + 150*I*(d*x^(1/3) + c)*b*c^4)*arctan2(sin(2*d*x^(1/3) + 2*c), cos(2*d*x^(1/3) + 2*c) + 1) - (-240*I*(d*x^(1/3) + c)^4*b + 600*I*(d*x^(1/3) + c)^3*b*c - 600*I*(d*x^(1/3) + c)^2*b*c^2 + 300*I*(d*x^(1/3) + c)*b*c^3 - 75*I*b*c^4)*dilog(-e^(2*I*d*x^(1/3) + 2*I*c)) - (48*(d*x^(1/3) + c)^5*b - 150*(d*x^(1/3) + c)^4*b*c + 200*(d*x^(1/3) + c)^3*b*c^2 - 150*(d*x^(1/3) + c)^2*b*c^3 + 75*(d*x^(1/3) + c)*b*c^4)*log(cos(2*d*x^(1/3) + 2*c)^2 + sin(2*d*x^(1/3) + 2*c)^2 + 2*cos(2*d*x^(1/3) + 2*c) + 1) + 360*I*b*polylog(6, -e^(2*I*d*x^(1/3) + 2*I*c)) + 90*(8*(d*x^(1/3) + c)*b - 5*b*c)*polylog(5, -e^(2*I*d*x^(1/3) + 2*I*c)) - (720*I*(d*x^(1/3) + c)^2*b - 900*I*(d*x^(1/3) + c)*b*c + 300*I*b*c^2)*polylog(4, -e^(2*I*d*x^(1/3) + 2*I*c)) - 30*(16*(d*x^(1/3) + c)^3*b - 30*(d*x^(1/3) + c)^2*b*c + 20*(d*x^(1/3) + c)*b*c^2 - 5*b*c^3)*polylog(3, -e^(2*I*d*x^(1/3) + 2*I*c)))/d^6","B",0
49,0,0,0,0.000000," ","integrate(a+b*tan(c+d*x^(1/3)),x, algorithm=""maxima"")","a x + 2 \, b \int \frac{\sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)}{\cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 1}\,{d x}"," ",0,"a*x + 2*b*integrate(sin(2*d*x^(1/3) + 2*c)/(cos(2*d*x^(1/3) + 2*c)^2 + sin(2*d*x^(1/3) + 2*c)^2 + 2*cos(2*d*x^(1/3) + 2*c) + 1), x)","F",0
50,0,0,0,0.000000," ","integrate((a+b*tan(c+d*x^(1/3)))/x,x, algorithm=""maxima"")","2 \, b \int \frac{\sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)}{{\left(\cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 1\right)} x}\,{d x} + a \log\left(x\right)"," ",0,"2*b*integrate(sin(2*d*x^(1/3) + 2*c)/((cos(2*d*x^(1/3) + 2*c)^2 + sin(2*d*x^(1/3) + 2*c)^2 + 2*cos(2*d*x^(1/3) + 2*c) + 1)*x), x) + a*log(x)","F",0
51,-1,0,0,0.000000," ","integrate((a+b*tan(c+d*x^(1/3)))/x^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
52,1,4673,0,2.160600," ","integrate(x^2*(a+b*tan(c+d*x^(1/3)))^2,x, algorithm=""maxima"")","\frac{{\left(d x^{\frac{1}{3}} + c\right)}^{9} a^{2} - 9 \, {\left(d x^{\frac{1}{3}} + c\right)}^{8} a^{2} c + 36 \, {\left(d x^{\frac{1}{3}} + c\right)}^{7} a^{2} c^{2} - 84 \, {\left(d x^{\frac{1}{3}} + c\right)}^{6} a^{2} c^{3} + 126 \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} a^{2} c^{4} - 126 \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} a^{2} c^{5} + 84 \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} a^{2} c^{6} - 36 \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} a^{2} c^{7} + 9 \, {\left(d x^{\frac{1}{3}} + c\right)} a^{2} c^{8} + 18 \, a b c^{8} \log\left(\sec\left(d x^{\frac{1}{3}} + c\right)\right) - \frac{9 \, {\left(-315 i \, {\left(d x^{\frac{1}{3}} + c\right)} b^{2} c^{8} - 35 \, {\left(2 \, a b + i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{9} + 315 \, {\left(2 \, a b + i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{8} c - 1260 \, {\left(2 \, a b + i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{7} c^{2} + 2940 \, {\left(2 \, a b + i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} c^{3} - 4410 \, {\left(2 \, a b + i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} c^{4} + 4410 \, {\left(2 \, a b + i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} c^{5} - 2940 \, {\left(2 \, a b + i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} c^{6} + 1260 \, {\left(2 \, a b + i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} c^{7} - 630 \, b^{2} c^{8} + {\left(10080 \, {\left(d x^{\frac{1}{3}} + c\right)}^{8} a b + 2520 \, b^{2} c^{7} - 23040 \, {\left(2 \, a b c + b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{7} + 94080 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} - 56448 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + 88200 \, {\left(a b c^{4} + 2 \, b^{2} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} - 23520 \, {\left(2 \, a b c^{5} + 5 \, b^{2} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + 17640 \, {\left(a b c^{6} + 3 \, b^{2} c^{5}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} - 2520 \, {\left(2 \, a b c^{7} + 7 \, b^{2} c^{6}\right)} {\left(d x^{\frac{1}{3}} + c\right)} + 24 \, {\left(420 \, {\left(d x^{\frac{1}{3}} + c\right)}^{8} a b + 105 \, b^{2} c^{7} - 960 \, {\left(2 \, a b c + b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{7} + 3920 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} - 2352 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + 3675 \, {\left(a b c^{4} + 2 \, b^{2} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} - 980 \, {\left(2 \, a b c^{5} + 5 \, b^{2} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + 735 \, {\left(a b c^{6} + 3 \, b^{2} c^{5}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} - 105 \, {\left(2 \, a b c^{7} + 7 \, b^{2} c^{6}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left(10080 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{8} a b + 2520 i \, b^{2} c^{7} + {\left(-46080 i \, a b c - 23040 i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{7} + {\left(94080 i \, a b c^{2} + 94080 i \, b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} + {\left(-112896 i \, a b c^{3} - 169344 i \, b^{2} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + {\left(88200 i \, a b c^{4} + 176400 i \, b^{2} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + {\left(-47040 i \, a b c^{5} - 117600 i \, b^{2} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left(17640 i \, a b c^{6} + 52920 i \, b^{2} c^{5}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left(-5040 i \, a b c^{7} - 17640 i \, b^{2} c^{6}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} \arctan\left(\sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right), \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 1\right) - {\left(35 \, {\left(2 \, a b + i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{9} - 315 \, {\left(2 \, b^{2} + {\left(2 \, a b + i \, b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{8} + 1260 \, {\left(4 \, b^{2} c + {\left(2 \, a b + i \, b^{2}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{7} - 2940 \, {\left(6 \, b^{2} c^{2} + {\left(2 \, a b + i \, b^{2}\right)} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} + 4410 \, {\left(8 \, b^{2} c^{3} + {\left(2 \, a b + i \, b^{2}\right)} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} - 4410 \, {\left(10 \, b^{2} c^{4} + {\left(2 \, a b + i \, b^{2}\right)} c^{5}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + 2940 \, {\left(12 \, b^{2} c^{5} + {\left(2 \, a b + i \, b^{2}\right)} c^{6}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} - 1260 \, {\left(14 \, b^{2} c^{6} + {\left(2 \, a b + i \, b^{2}\right)} c^{7}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} - {\left(-315 i \, b^{2} c^{8} - 5040 \, b^{2} c^{7}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - {\left(40320 \, {\left(d x^{\frac{1}{3}} + c\right)}^{7} a b - 2520 \, a b c^{7} - 8820 \, b^{2} c^{6} - 80640 \, {\left(2 \, a b c + b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} + 282240 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} - 141120 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + 176400 \, {\left(a b c^{4} + 2 \, b^{2} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} - 35280 \, {\left(2 \, a b c^{5} + 5 \, b^{2} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + 17640 \, {\left(a b c^{6} + 3 \, b^{2} c^{5}\right)} {\left(d x^{\frac{1}{3}} + c\right)} + 1260 \, {\left(32 \, {\left(d x^{\frac{1}{3}} + c\right)}^{7} a b - 2 \, a b c^{7} - 7 \, b^{2} c^{6} - 64 \, {\left(2 \, a b c + b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} + 224 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} - 112 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + 140 \, {\left(a b c^{4} + 2 \, b^{2} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} - 28 \, {\left(2 \, a b c^{5} + 5 \, b^{2} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + 14 \, {\left(a b c^{6} + 3 \, b^{2} c^{5}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - {\left(-40320 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{7} a b + 2520 i \, a b c^{7} + 8820 i \, b^{2} c^{6} + {\left(161280 i \, a b c + 80640 i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} + {\left(-282240 i \, a b c^{2} - 282240 i \, b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + {\left(282240 i \, a b c^{3} + 423360 i \, b^{2} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + {\left(-176400 i \, a b c^{4} - 352800 i \, b^{2} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left(70560 i \, a b c^{5} + 176400 i \, b^{2} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left(-17640 i \, a b c^{6} - 52920 i \, b^{2} c^{5}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} {\rm Li}_2\left(-e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}\right) + {\left(-5040 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{8} a b - 1260 i \, b^{2} c^{7} + {\left(23040 i \, a b c + 11520 i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{7} + {\left(-47040 i \, a b c^{2} - 47040 i \, b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} + {\left(56448 i \, a b c^{3} + 84672 i \, b^{2} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + {\left(-44100 i \, a b c^{4} - 88200 i \, b^{2} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + {\left(23520 i \, a b c^{5} + 58800 i \, b^{2} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left(-8820 i \, a b c^{6} - 26460 i \, b^{2} c^{5}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left(2520 i \, a b c^{7} + 8820 i \, b^{2} c^{6}\right)} {\left(d x^{\frac{1}{3}} + c\right)} + {\left(-5040 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{8} a b - 1260 i \, b^{2} c^{7} + {\left(23040 i \, a b c + 11520 i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{7} + {\left(-47040 i \, a b c^{2} - 47040 i \, b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} + {\left(56448 i \, a b c^{3} + 84672 i \, b^{2} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + {\left(-44100 i \, a b c^{4} - 88200 i \, b^{2} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + {\left(23520 i \, a b c^{5} + 58800 i \, b^{2} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left(-8820 i \, a b c^{6} - 26460 i \, b^{2} c^{5}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left(2520 i \, a b c^{7} + 8820 i \, b^{2} c^{6}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 12 \, {\left(420 \, {\left(d x^{\frac{1}{3}} + c\right)}^{8} a b + 105 \, b^{2} c^{7} - 960 \, {\left(2 \, a b c + b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{7} + 3920 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} - 2352 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + 3675 \, {\left(a b c^{4} + 2 \, b^{2} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} - 980 \, {\left(2 \, a b c^{5} + 5 \, b^{2} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + 735 \, {\left(a b c^{6} + 3 \, b^{2} c^{5}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} - 105 \, {\left(2 \, a b c^{7} + 7 \, b^{2} c^{6}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} \log\left(\cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 1\right) + {\left(1587600 i \, a b \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - 1587600 \, a b \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 1587600 i \, a b\right)} {\rm Li}_{9}(-e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}) + {\left(3175200 \, {\left(d x^{\frac{1}{3}} + c\right)} a b - 1814400 \, a b c - 907200 \, b^{2} + 453600 \, {\left(7 \, {\left(d x^{\frac{1}{3}} + c\right)} a b - 4 \, a b c - 2 \, b^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left(3175200 i \, {\left(d x^{\frac{1}{3}} + c\right)} a b - 1814400 i \, a b c - 907200 i \, b^{2}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} {\rm Li}_{8}(-e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}) + {\left(-3175200 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} a b - 1058400 i \, a b c^{2} - 1058400 i \, b^{2} c + {\left(3628800 i \, a b c + 1814400 i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)} + {\left(-3175200 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} a b - 1058400 i \, a b c^{2} - 1058400 i \, b^{2} c + {\left(3628800 i \, a b c + 1814400 i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 151200 \, {\left(21 \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} a b + 7 \, a b c^{2} + 7 \, b^{2} c - 12 \, {\left(2 \, a b c + b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} {\rm Li}_{7}(-e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}) - {\left(2116800 \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} a b - 423360 \, a b c^{3} - 635040 \, b^{2} c^{2} - 1814400 \, {\left(2 \, a b c + b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + 2116800 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)} + 30240 \, {\left(70 \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} a b - 14 \, a b c^{3} - 21 \, b^{2} c^{2} - 60 \, {\left(2 \, a b c + b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + 70 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - {\left(-2116800 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} a b + 423360 i \, a b c^{3} + 635040 i \, b^{2} c^{2} + {\left(3628800 i \, a b c + 1814400 i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left(-2116800 i \, a b c^{2} - 2116800 i \, b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} {\rm Li}_{6}(-e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}) + {\left(1058400 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} a b + 132300 i \, a b c^{4} + 264600 i \, b^{2} c^{3} + {\left(-2419200 i \, a b c - 1209600 i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left(2116800 i \, a b c^{2} + 2116800 i \, b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left(-846720 i \, a b c^{3} - 1270080 i \, b^{2} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)} + {\left(1058400 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} a b + 132300 i \, a b c^{4} + 264600 i \, b^{2} c^{3} + {\left(-2419200 i \, a b c - 1209600 i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left(2116800 i \, a b c^{2} + 2116800 i \, b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left(-846720 i \, a b c^{3} - 1270080 i \, b^{2} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - 3780 \, {\left(280 \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} a b + 35 \, a b c^{4} + 70 \, b^{2} c^{3} - 320 \, {\left(2 \, a b c + b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + 560 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} - 112 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} {\rm Li}_{5}(-e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}) + {\left(423360 \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} a b - 35280 \, a b c^{5} - 88200 \, b^{2} c^{4} - 604800 \, {\left(2 \, a b c + b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + 1411200 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} - 423360 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + 264600 \, {\left(a b c^{4} + 2 \, b^{2} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)} + 2520 \, {\left(168 \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} a b - 14 \, a b c^{5} - 35 \, b^{2} c^{4} - 240 \, {\left(2 \, a b c + b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + 560 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} - 168 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + 105 \, {\left(a b c^{4} + 2 \, b^{2} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left(423360 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} a b - 35280 i \, a b c^{5} - 88200 i \, b^{2} c^{4} + {\left(-1209600 i \, a b c - 604800 i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + {\left(1411200 i \, a b c^{2} + 1411200 i \, b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left(-846720 i \, a b c^{3} - 1270080 i \, b^{2} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left(264600 i \, a b c^{4} + 529200 i \, b^{2} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} {\rm Li}_{4}(-e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}) + {\left(-141120 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{6} a b - 8820 i \, a b c^{6} - 26460 i \, b^{2} c^{5} + {\left(483840 i \, a b c + 241920 i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + {\left(-705600 i \, a b c^{2} - 705600 i \, b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + {\left(564480 i \, a b c^{3} + 846720 i \, b^{2} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left(-264600 i \, a b c^{4} - 529200 i \, b^{2} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left(70560 i \, a b c^{5} + 176400 i \, b^{2} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)} + {\left(-141120 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{6} a b - 8820 i \, a b c^{6} - 26460 i \, b^{2} c^{5} + {\left(483840 i \, a b c + 241920 i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + {\left(-705600 i \, a b c^{2} - 705600 i \, b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + {\left(564480 i \, a b c^{3} + 846720 i \, b^{2} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left(-264600 i \, a b c^{4} - 529200 i \, b^{2} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left(70560 i \, a b c^{5} + 176400 i \, b^{2} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 1260 \, {\left(112 \, {\left(d x^{\frac{1}{3}} + c\right)}^{6} a b + 7 \, a b c^{6} + 21 \, b^{2} c^{5} - 192 \, {\left(2 \, a b c + b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + 560 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} - 224 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + 210 \, {\left(a b c^{4} + 2 \, b^{2} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} - 28 \, {\left(2 \, a b c^{5} + 5 \, b^{2} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} {\rm Li}_{3}(-e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}) + {\left({\left(-70 i \, a b + 35 \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{9} + {\left(630 i \, b^{2} + {\left(630 i \, a b - 315 \, b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{8} + {\left(-5040 i \, b^{2} c + {\left(-2520 i \, a b + 1260 \, b^{2}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{7} + {\left(17640 i \, b^{2} c^{2} + {\left(5880 i \, a b - 2940 \, b^{2}\right)} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} + {\left(-35280 i \, b^{2} c^{3} + {\left(-8820 i \, a b + 4410 \, b^{2}\right)} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + {\left(44100 i \, b^{2} c^{4} + {\left(8820 i \, a b - 4410 \, b^{2}\right)} c^{5}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + {\left(-35280 i \, b^{2} c^{5} + {\left(-5880 i \, a b + 2940 \, b^{2}\right)} c^{6}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left(17640 i \, b^{2} c^{6} + {\left(2520 i \, a b - 1260 \, b^{2}\right)} c^{7}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + 315 \, {\left(b^{2} c^{8} - 16 i \, b^{2} c^{7}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)}}{-315 i \, \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 315 \, \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - 315 i}}{3 \, d^{9}}"," ",0,"1/3*((d*x^(1/3) + c)^9*a^2 - 9*(d*x^(1/3) + c)^8*a^2*c + 36*(d*x^(1/3) + c)^7*a^2*c^2 - 84*(d*x^(1/3) + c)^6*a^2*c^3 + 126*(d*x^(1/3) + c)^5*a^2*c^4 - 126*(d*x^(1/3) + c)^4*a^2*c^5 + 84*(d*x^(1/3) + c)^3*a^2*c^6 - 36*(d*x^(1/3) + c)^2*a^2*c^7 + 9*(d*x^(1/3) + c)*a^2*c^8 + 18*a*b*c^8*log(sec(d*x^(1/3) + c)) - 9*(-315*I*(d*x^(1/3) + c)*b^2*c^8 - 35*(2*a*b + I*b^2)*(d*x^(1/3) + c)^9 + 315*(2*a*b + I*b^2)*(d*x^(1/3) + c)^8*c - 1260*(2*a*b + I*b^2)*(d*x^(1/3) + c)^7*c^2 + 2940*(2*a*b + I*b^2)*(d*x^(1/3) + c)^6*c^3 - 4410*(2*a*b + I*b^2)*(d*x^(1/3) + c)^5*c^4 + 4410*(2*a*b + I*b^2)*(d*x^(1/3) + c)^4*c^5 - 2940*(2*a*b + I*b^2)*(d*x^(1/3) + c)^3*c^6 + 1260*(2*a*b + I*b^2)*(d*x^(1/3) + c)^2*c^7 - 630*b^2*c^8 + (10080*(d*x^(1/3) + c)^8*a*b + 2520*b^2*c^7 - 23040*(2*a*b*c + b^2)*(d*x^(1/3) + c)^7 + 94080*(a*b*c^2 + b^2*c)*(d*x^(1/3) + c)^6 - 56448*(2*a*b*c^3 + 3*b^2*c^2)*(d*x^(1/3) + c)^5 + 88200*(a*b*c^4 + 2*b^2*c^3)*(d*x^(1/3) + c)^4 - 23520*(2*a*b*c^5 + 5*b^2*c^4)*(d*x^(1/3) + c)^3 + 17640*(a*b*c^6 + 3*b^2*c^5)*(d*x^(1/3) + c)^2 - 2520*(2*a*b*c^7 + 7*b^2*c^6)*(d*x^(1/3) + c) + 24*(420*(d*x^(1/3) + c)^8*a*b + 105*b^2*c^7 - 960*(2*a*b*c + b^2)*(d*x^(1/3) + c)^7 + 3920*(a*b*c^2 + b^2*c)*(d*x^(1/3) + c)^6 - 2352*(2*a*b*c^3 + 3*b^2*c^2)*(d*x^(1/3) + c)^5 + 3675*(a*b*c^4 + 2*b^2*c^3)*(d*x^(1/3) + c)^4 - 980*(2*a*b*c^5 + 5*b^2*c^4)*(d*x^(1/3) + c)^3 + 735*(a*b*c^6 + 3*b^2*c^5)*(d*x^(1/3) + c)^2 - 105*(2*a*b*c^7 + 7*b^2*c^6)*(d*x^(1/3) + c))*cos(2*d*x^(1/3) + 2*c) + (10080*I*(d*x^(1/3) + c)^8*a*b + 2520*I*b^2*c^7 + (-46080*I*a*b*c - 23040*I*b^2)*(d*x^(1/3) + c)^7 + (94080*I*a*b*c^2 + 94080*I*b^2*c)*(d*x^(1/3) + c)^6 + (-112896*I*a*b*c^3 - 169344*I*b^2*c^2)*(d*x^(1/3) + c)^5 + (88200*I*a*b*c^4 + 176400*I*b^2*c^3)*(d*x^(1/3) + c)^4 + (-47040*I*a*b*c^5 - 117600*I*b^2*c^4)*(d*x^(1/3) + c)^3 + (17640*I*a*b*c^6 + 52920*I*b^2*c^5)*(d*x^(1/3) + c)^2 + (-5040*I*a*b*c^7 - 17640*I*b^2*c^6)*(d*x^(1/3) + c))*sin(2*d*x^(1/3) + 2*c))*arctan2(sin(2*d*x^(1/3) + 2*c), cos(2*d*x^(1/3) + 2*c) + 1) - (35*(2*a*b + I*b^2)*(d*x^(1/3) + c)^9 - 315*(2*b^2 + (2*a*b + I*b^2)*c)*(d*x^(1/3) + c)^8 + 1260*(4*b^2*c + (2*a*b + I*b^2)*c^2)*(d*x^(1/3) + c)^7 - 2940*(6*b^2*c^2 + (2*a*b + I*b^2)*c^3)*(d*x^(1/3) + c)^6 + 4410*(8*b^2*c^3 + (2*a*b + I*b^2)*c^4)*(d*x^(1/3) + c)^5 - 4410*(10*b^2*c^4 + (2*a*b + I*b^2)*c^5)*(d*x^(1/3) + c)^4 + 2940*(12*b^2*c^5 + (2*a*b + I*b^2)*c^6)*(d*x^(1/3) + c)^3 - 1260*(14*b^2*c^6 + (2*a*b + I*b^2)*c^7)*(d*x^(1/3) + c)^2 - (-315*I*b^2*c^8 - 5040*b^2*c^7)*(d*x^(1/3) + c))*cos(2*d*x^(1/3) + 2*c) - (40320*(d*x^(1/3) + c)^7*a*b - 2520*a*b*c^7 - 8820*b^2*c^6 - 80640*(2*a*b*c + b^2)*(d*x^(1/3) + c)^6 + 282240*(a*b*c^2 + b^2*c)*(d*x^(1/3) + c)^5 - 141120*(2*a*b*c^3 + 3*b^2*c^2)*(d*x^(1/3) + c)^4 + 176400*(a*b*c^4 + 2*b^2*c^3)*(d*x^(1/3) + c)^3 - 35280*(2*a*b*c^5 + 5*b^2*c^4)*(d*x^(1/3) + c)^2 + 17640*(a*b*c^6 + 3*b^2*c^5)*(d*x^(1/3) + c) + 1260*(32*(d*x^(1/3) + c)^7*a*b - 2*a*b*c^7 - 7*b^2*c^6 - 64*(2*a*b*c + b^2)*(d*x^(1/3) + c)^6 + 224*(a*b*c^2 + b^2*c)*(d*x^(1/3) + c)^5 - 112*(2*a*b*c^3 + 3*b^2*c^2)*(d*x^(1/3) + c)^4 + 140*(a*b*c^4 + 2*b^2*c^3)*(d*x^(1/3) + c)^3 - 28*(2*a*b*c^5 + 5*b^2*c^4)*(d*x^(1/3) + c)^2 + 14*(a*b*c^6 + 3*b^2*c^5)*(d*x^(1/3) + c))*cos(2*d*x^(1/3) + 2*c) - (-40320*I*(d*x^(1/3) + c)^7*a*b + 2520*I*a*b*c^7 + 8820*I*b^2*c^6 + (161280*I*a*b*c + 80640*I*b^2)*(d*x^(1/3) + c)^6 + (-282240*I*a*b*c^2 - 282240*I*b^2*c)*(d*x^(1/3) + c)^5 + (282240*I*a*b*c^3 + 423360*I*b^2*c^2)*(d*x^(1/3) + c)^4 + (-176400*I*a*b*c^4 - 352800*I*b^2*c^3)*(d*x^(1/3) + c)^3 + (70560*I*a*b*c^5 + 176400*I*b^2*c^4)*(d*x^(1/3) + c)^2 + (-17640*I*a*b*c^6 - 52920*I*b^2*c^5)*(d*x^(1/3) + c))*sin(2*d*x^(1/3) + 2*c))*dilog(-e^(2*I*d*x^(1/3) + 2*I*c)) + (-5040*I*(d*x^(1/3) + c)^8*a*b - 1260*I*b^2*c^7 + (23040*I*a*b*c + 11520*I*b^2)*(d*x^(1/3) + c)^7 + (-47040*I*a*b*c^2 - 47040*I*b^2*c)*(d*x^(1/3) + c)^6 + (56448*I*a*b*c^3 + 84672*I*b^2*c^2)*(d*x^(1/3) + c)^5 + (-44100*I*a*b*c^4 - 88200*I*b^2*c^3)*(d*x^(1/3) + c)^4 + (23520*I*a*b*c^5 + 58800*I*b^2*c^4)*(d*x^(1/3) + c)^3 + (-8820*I*a*b*c^6 - 26460*I*b^2*c^5)*(d*x^(1/3) + c)^2 + (2520*I*a*b*c^7 + 8820*I*b^2*c^6)*(d*x^(1/3) + c) + (-5040*I*(d*x^(1/3) + c)^8*a*b - 1260*I*b^2*c^7 + (23040*I*a*b*c + 11520*I*b^2)*(d*x^(1/3) + c)^7 + (-47040*I*a*b*c^2 - 47040*I*b^2*c)*(d*x^(1/3) + c)^6 + (56448*I*a*b*c^3 + 84672*I*b^2*c^2)*(d*x^(1/3) + c)^5 + (-44100*I*a*b*c^4 - 88200*I*b^2*c^3)*(d*x^(1/3) + c)^4 + (23520*I*a*b*c^5 + 58800*I*b^2*c^4)*(d*x^(1/3) + c)^3 + (-8820*I*a*b*c^6 - 26460*I*b^2*c^5)*(d*x^(1/3) + c)^2 + (2520*I*a*b*c^7 + 8820*I*b^2*c^6)*(d*x^(1/3) + c))*cos(2*d*x^(1/3) + 2*c) + 12*(420*(d*x^(1/3) + c)^8*a*b + 105*b^2*c^7 - 960*(2*a*b*c + b^2)*(d*x^(1/3) + c)^7 + 3920*(a*b*c^2 + b^2*c)*(d*x^(1/3) + c)^6 - 2352*(2*a*b*c^3 + 3*b^2*c^2)*(d*x^(1/3) + c)^5 + 3675*(a*b*c^4 + 2*b^2*c^3)*(d*x^(1/3) + c)^4 - 980*(2*a*b*c^5 + 5*b^2*c^4)*(d*x^(1/3) + c)^3 + 735*(a*b*c^6 + 3*b^2*c^5)*(d*x^(1/3) + c)^2 - 105*(2*a*b*c^7 + 7*b^2*c^6)*(d*x^(1/3) + c))*sin(2*d*x^(1/3) + 2*c))*log(cos(2*d*x^(1/3) + 2*c)^2 + sin(2*d*x^(1/3) + 2*c)^2 + 2*cos(2*d*x^(1/3) + 2*c) + 1) + (1587600*I*a*b*cos(2*d*x^(1/3) + 2*c) - 1587600*a*b*sin(2*d*x^(1/3) + 2*c) + 1587600*I*a*b)*polylog(9, -e^(2*I*d*x^(1/3) + 2*I*c)) + (3175200*(d*x^(1/3) + c)*a*b - 1814400*a*b*c - 907200*b^2 + 453600*(7*(d*x^(1/3) + c)*a*b - 4*a*b*c - 2*b^2)*cos(2*d*x^(1/3) + 2*c) + (3175200*I*(d*x^(1/3) + c)*a*b - 1814400*I*a*b*c - 907200*I*b^2)*sin(2*d*x^(1/3) + 2*c))*polylog(8, -e^(2*I*d*x^(1/3) + 2*I*c)) + (-3175200*I*(d*x^(1/3) + c)^2*a*b - 1058400*I*a*b*c^2 - 1058400*I*b^2*c + (3628800*I*a*b*c + 1814400*I*b^2)*(d*x^(1/3) + c) + (-3175200*I*(d*x^(1/3) + c)^2*a*b - 1058400*I*a*b*c^2 - 1058400*I*b^2*c + (3628800*I*a*b*c + 1814400*I*b^2)*(d*x^(1/3) + c))*cos(2*d*x^(1/3) + 2*c) + 151200*(21*(d*x^(1/3) + c)^2*a*b + 7*a*b*c^2 + 7*b^2*c - 12*(2*a*b*c + b^2)*(d*x^(1/3) + c))*sin(2*d*x^(1/3) + 2*c))*polylog(7, -e^(2*I*d*x^(1/3) + 2*I*c)) - (2116800*(d*x^(1/3) + c)^3*a*b - 423360*a*b*c^3 - 635040*b^2*c^2 - 1814400*(2*a*b*c + b^2)*(d*x^(1/3) + c)^2 + 2116800*(a*b*c^2 + b^2*c)*(d*x^(1/3) + c) + 30240*(70*(d*x^(1/3) + c)^3*a*b - 14*a*b*c^3 - 21*b^2*c^2 - 60*(2*a*b*c + b^2)*(d*x^(1/3) + c)^2 + 70*(a*b*c^2 + b^2*c)*(d*x^(1/3) + c))*cos(2*d*x^(1/3) + 2*c) - (-2116800*I*(d*x^(1/3) + c)^3*a*b + 423360*I*a*b*c^3 + 635040*I*b^2*c^2 + (3628800*I*a*b*c + 1814400*I*b^2)*(d*x^(1/3) + c)^2 + (-2116800*I*a*b*c^2 - 2116800*I*b^2*c)*(d*x^(1/3) + c))*sin(2*d*x^(1/3) + 2*c))*polylog(6, -e^(2*I*d*x^(1/3) + 2*I*c)) + (1058400*I*(d*x^(1/3) + c)^4*a*b + 132300*I*a*b*c^4 + 264600*I*b^2*c^3 + (-2419200*I*a*b*c - 1209600*I*b^2)*(d*x^(1/3) + c)^3 + (2116800*I*a*b*c^2 + 2116800*I*b^2*c)*(d*x^(1/3) + c)^2 + (-846720*I*a*b*c^3 - 1270080*I*b^2*c^2)*(d*x^(1/3) + c) + (1058400*I*(d*x^(1/3) + c)^4*a*b + 132300*I*a*b*c^4 + 264600*I*b^2*c^3 + (-2419200*I*a*b*c - 1209600*I*b^2)*(d*x^(1/3) + c)^3 + (2116800*I*a*b*c^2 + 2116800*I*b^2*c)*(d*x^(1/3) + c)^2 + (-846720*I*a*b*c^3 - 1270080*I*b^2*c^2)*(d*x^(1/3) + c))*cos(2*d*x^(1/3) + 2*c) - 3780*(280*(d*x^(1/3) + c)^4*a*b + 35*a*b*c^4 + 70*b^2*c^3 - 320*(2*a*b*c + b^2)*(d*x^(1/3) + c)^3 + 560*(a*b*c^2 + b^2*c)*(d*x^(1/3) + c)^2 - 112*(2*a*b*c^3 + 3*b^2*c^2)*(d*x^(1/3) + c))*sin(2*d*x^(1/3) + 2*c))*polylog(5, -e^(2*I*d*x^(1/3) + 2*I*c)) + (423360*(d*x^(1/3) + c)^5*a*b - 35280*a*b*c^5 - 88200*b^2*c^4 - 604800*(2*a*b*c + b^2)*(d*x^(1/3) + c)^4 + 1411200*(a*b*c^2 + b^2*c)*(d*x^(1/3) + c)^3 - 423360*(2*a*b*c^3 + 3*b^2*c^2)*(d*x^(1/3) + c)^2 + 264600*(a*b*c^4 + 2*b^2*c^3)*(d*x^(1/3) + c) + 2520*(168*(d*x^(1/3) + c)^5*a*b - 14*a*b*c^5 - 35*b^2*c^4 - 240*(2*a*b*c + b^2)*(d*x^(1/3) + c)^4 + 560*(a*b*c^2 + b^2*c)*(d*x^(1/3) + c)^3 - 168*(2*a*b*c^3 + 3*b^2*c^2)*(d*x^(1/3) + c)^2 + 105*(a*b*c^4 + 2*b^2*c^3)*(d*x^(1/3) + c))*cos(2*d*x^(1/3) + 2*c) + (423360*I*(d*x^(1/3) + c)^5*a*b - 35280*I*a*b*c^5 - 88200*I*b^2*c^4 + (-1209600*I*a*b*c - 604800*I*b^2)*(d*x^(1/3) + c)^4 + (1411200*I*a*b*c^2 + 1411200*I*b^2*c)*(d*x^(1/3) + c)^3 + (-846720*I*a*b*c^3 - 1270080*I*b^2*c^2)*(d*x^(1/3) + c)^2 + (264600*I*a*b*c^4 + 529200*I*b^2*c^3)*(d*x^(1/3) + c))*sin(2*d*x^(1/3) + 2*c))*polylog(4, -e^(2*I*d*x^(1/3) + 2*I*c)) + (-141120*I*(d*x^(1/3) + c)^6*a*b - 8820*I*a*b*c^6 - 26460*I*b^2*c^5 + (483840*I*a*b*c + 241920*I*b^2)*(d*x^(1/3) + c)^5 + (-705600*I*a*b*c^2 - 705600*I*b^2*c)*(d*x^(1/3) + c)^4 + (564480*I*a*b*c^3 + 846720*I*b^2*c^2)*(d*x^(1/3) + c)^3 + (-264600*I*a*b*c^4 - 529200*I*b^2*c^3)*(d*x^(1/3) + c)^2 + (70560*I*a*b*c^5 + 176400*I*b^2*c^4)*(d*x^(1/3) + c) + (-141120*I*(d*x^(1/3) + c)^6*a*b - 8820*I*a*b*c^6 - 26460*I*b^2*c^5 + (483840*I*a*b*c + 241920*I*b^2)*(d*x^(1/3) + c)^5 + (-705600*I*a*b*c^2 - 705600*I*b^2*c)*(d*x^(1/3) + c)^4 + (564480*I*a*b*c^3 + 846720*I*b^2*c^2)*(d*x^(1/3) + c)^3 + (-264600*I*a*b*c^4 - 529200*I*b^2*c^3)*(d*x^(1/3) + c)^2 + (70560*I*a*b*c^5 + 176400*I*b^2*c^4)*(d*x^(1/3) + c))*cos(2*d*x^(1/3) + 2*c) + 1260*(112*(d*x^(1/3) + c)^6*a*b + 7*a*b*c^6 + 21*b^2*c^5 - 192*(2*a*b*c + b^2)*(d*x^(1/3) + c)^5 + 560*(a*b*c^2 + b^2*c)*(d*x^(1/3) + c)^4 - 224*(2*a*b*c^3 + 3*b^2*c^2)*(d*x^(1/3) + c)^3 + 210*(a*b*c^4 + 2*b^2*c^3)*(d*x^(1/3) + c)^2 - 28*(2*a*b*c^5 + 5*b^2*c^4)*(d*x^(1/3) + c))*sin(2*d*x^(1/3) + 2*c))*polylog(3, -e^(2*I*d*x^(1/3) + 2*I*c)) + ((-70*I*a*b + 35*b^2)*(d*x^(1/3) + c)^9 + (630*I*b^2 + (630*I*a*b - 315*b^2)*c)*(d*x^(1/3) + c)^8 + (-5040*I*b^2*c + (-2520*I*a*b + 1260*b^2)*c^2)*(d*x^(1/3) + c)^7 + (17640*I*b^2*c^2 + (5880*I*a*b - 2940*b^2)*c^3)*(d*x^(1/3) + c)^6 + (-35280*I*b^2*c^3 + (-8820*I*a*b + 4410*b^2)*c^4)*(d*x^(1/3) + c)^5 + (44100*I*b^2*c^4 + (8820*I*a*b - 4410*b^2)*c^5)*(d*x^(1/3) + c)^4 + (-35280*I*b^2*c^5 + (-5880*I*a*b + 2940*b^2)*c^6)*(d*x^(1/3) + c)^3 + (17640*I*b^2*c^6 + (2520*I*a*b - 1260*b^2)*c^7)*(d*x^(1/3) + c)^2 + 315*(b^2*c^8 - 16*I*b^2*c^7)*(d*x^(1/3) + c))*sin(2*d*x^(1/3) + 2*c))/(-315*I*cos(2*d*x^(1/3) + 2*c) + 315*sin(2*d*x^(1/3) + 2*c) - 315*I))/d^9","B",0
53,1,2402,0,1.436885," ","integrate(x*(a+b*tan(c+d*x^(1/3)))^2,x, algorithm=""maxima"")","\frac{{\left(d x^{\frac{1}{3}} + c\right)}^{6} a^{2} - 6 \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} a^{2} c + 15 \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} a^{2} c^{2} - 20 \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} a^{2} c^{3} + 15 \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} a^{2} c^{4} - 6 \, {\left(d x^{\frac{1}{3}} + c\right)} a^{2} c^{5} - 12 \, a b c^{5} \log\left(\sec\left(d x^{\frac{1}{3}} + c\right)\right) - \frac{6 \, {\left(30 i \, {\left(d x^{\frac{1}{3}} + c\right)} b^{2} c^{5} - 5 \, {\left(2 \, a b + i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} + 30 \, {\left(2 \, a b + i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} c - 75 \, {\left(2 \, a b + i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} c^{2} + 100 \, {\left(2 \, a b + i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} c^{3} - 75 \, {\left(2 \, a b + i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} c^{4} + 60 \, b^{2} c^{5} + {\left(192 \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} a b - 150 \, b^{2} c^{4} - 300 \, {\left(2 \, a b c + b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + 800 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} - 300 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + 300 \, {\left(a b c^{4} + 2 \, b^{2} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)} + 2 \, {\left(96 \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} a b - 75 \, b^{2} c^{4} - 150 \, {\left(2 \, a b c + b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + 400 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} - 150 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + 150 \, {\left(a b c^{4} + 2 \, b^{2} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left(192 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} a b - 150 i \, b^{2} c^{4} + {\left(-600 i \, a b c - 300 i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + {\left(800 i \, a b c^{2} + 800 i \, b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left(-600 i \, a b c^{3} - 900 i \, b^{2} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left(300 i \, a b c^{4} + 600 i \, b^{2} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} \arctan\left(\sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right), \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 1\right) - 5 \, {\left({\left(2 \, a b + i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} - 6 \, {\left(2 \, b^{2} + {\left(2 \, a b + i \, b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + 15 \, {\left(4 \, b^{2} c + {\left(2 \, a b + i \, b^{2}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} - 20 \, {\left(6 \, b^{2} c^{2} + {\left(2 \, a b + i \, b^{2}\right)} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + 15 \, {\left(8 \, b^{2} c^{3} + {\left(2 \, a b + i \, b^{2}\right)} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + 6 \, {\left(-i \, b^{2} c^{5} - 10 \, b^{2} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - {\left(480 \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} a b + 150 \, a b c^{4} + 300 \, b^{2} c^{3} - 600 \, {\left(2 \, a b c + b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + 1200 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} - 300 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)} + 30 \, {\left(16 \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} a b + 5 \, a b c^{4} + 10 \, b^{2} c^{3} - 20 \, {\left(2 \, a b c + b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + 40 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} - 10 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - {\left(-480 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} a b - 150 i \, a b c^{4} - 300 i \, b^{2} c^{3} + {\left(1200 i \, a b c + 600 i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left(-1200 i \, a b c^{2} - 1200 i \, b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left(600 i \, a b c^{3} + 900 i \, b^{2} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} {\rm Li}_2\left(-e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}\right) + {\left(-96 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} a b + 75 i \, b^{2} c^{4} + {\left(300 i \, a b c + 150 i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + {\left(-400 i \, a b c^{2} - 400 i \, b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left(300 i \, a b c^{3} + 450 i \, b^{2} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left(-150 i \, a b c^{4} - 300 i \, b^{2} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)} + {\left(-96 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} a b + 75 i \, b^{2} c^{4} + {\left(300 i \, a b c + 150 i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + {\left(-400 i \, a b c^{2} - 400 i \, b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left(300 i \, a b c^{3} + 450 i \, b^{2} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left(-150 i \, a b c^{4} - 300 i \, b^{2} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left(96 \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} a b - 75 \, b^{2} c^{4} - 150 \, {\left(2 \, a b c + b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + 400 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} - 150 \, {\left(2 \, a b c^{3} + 3 \, b^{2} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + 150 \, {\left(a b c^{4} + 2 \, b^{2} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} \log\left(\cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 1\right) - {\left(720 \, a b \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 720 i \, a b \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 720 \, a b\right)} {\rm Li}_{6}(-e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}) + {\left(1440 i \, {\left(d x^{\frac{1}{3}} + c\right)} a b - 900 i \, a b c - 450 i \, b^{2} + {\left(1440 i \, {\left(d x^{\frac{1}{3}} + c\right)} a b - 900 i \, a b c - 450 i \, b^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - 90 \, {\left(16 \, {\left(d x^{\frac{1}{3}} + c\right)} a b - 10 \, a b c - 5 \, b^{2}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} {\rm Li}_{5}(-e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}) + {\left(1440 \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} a b + 600 \, a b c^{2} + 600 \, b^{2} c - 900 \, {\left(2 \, a b c + b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)} + 60 \, {\left(24 \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} a b + 10 \, a b c^{2} + 10 \, b^{2} c - 15 \, {\left(2 \, a b c + b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left(1440 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} a b + 600 i \, a b c^{2} + 600 i \, b^{2} c + {\left(-1800 i \, a b c - 900 i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} {\rm Li}_{4}(-e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}) + {\left(-960 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} a b + 300 i \, a b c^{3} + 450 i \, b^{2} c^{2} + {\left(1800 i \, a b c + 900 i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left(-1200 i \, a b c^{2} - 1200 i \, b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)} + {\left(-960 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} a b + 300 i \, a b c^{3} + 450 i \, b^{2} c^{2} + {\left(1800 i \, a b c + 900 i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left(-1200 i \, a b c^{2} - 1200 i \, b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 30 \, {\left(32 \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} a b - 10 \, a b c^{3} - 15 \, b^{2} c^{2} - 30 \, {\left(2 \, a b c + b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + 40 \, {\left(a b c^{2} + b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} {\rm Li}_{3}(-e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}) + {\left({\left(-10 i \, a b + 5 \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} + {\left(60 i \, b^{2} + {\left(60 i \, a b - 30 \, b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + {\left(-300 i \, b^{2} c + {\left(-150 i \, a b + 75 \, b^{2}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + {\left(600 i \, b^{2} c^{2} + {\left(200 i \, a b - 100 \, b^{2}\right)} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left(-600 i \, b^{2} c^{3} + {\left(-150 i \, a b + 75 \, b^{2}\right)} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} - {\left(30 \, b^{2} c^{5} - 300 i \, b^{2} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)}}{-30 i \, \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 30 \, \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - 30 i}}{2 \, d^{6}}"," ",0,"1/2*((d*x^(1/3) + c)^6*a^2 - 6*(d*x^(1/3) + c)^5*a^2*c + 15*(d*x^(1/3) + c)^4*a^2*c^2 - 20*(d*x^(1/3) + c)^3*a^2*c^3 + 15*(d*x^(1/3) + c)^2*a^2*c^4 - 6*(d*x^(1/3) + c)*a^2*c^5 - 12*a*b*c^5*log(sec(d*x^(1/3) + c)) - 6*(30*I*(d*x^(1/3) + c)*b^2*c^5 - 5*(2*a*b + I*b^2)*(d*x^(1/3) + c)^6 + 30*(2*a*b + I*b^2)*(d*x^(1/3) + c)^5*c - 75*(2*a*b + I*b^2)*(d*x^(1/3) + c)^4*c^2 + 100*(2*a*b + I*b^2)*(d*x^(1/3) + c)^3*c^3 - 75*(2*a*b + I*b^2)*(d*x^(1/3) + c)^2*c^4 + 60*b^2*c^5 + (192*(d*x^(1/3) + c)^5*a*b - 150*b^2*c^4 - 300*(2*a*b*c + b^2)*(d*x^(1/3) + c)^4 + 800*(a*b*c^2 + b^2*c)*(d*x^(1/3) + c)^3 - 300*(2*a*b*c^3 + 3*b^2*c^2)*(d*x^(1/3) + c)^2 + 300*(a*b*c^4 + 2*b^2*c^3)*(d*x^(1/3) + c) + 2*(96*(d*x^(1/3) + c)^5*a*b - 75*b^2*c^4 - 150*(2*a*b*c + b^2)*(d*x^(1/3) + c)^4 + 400*(a*b*c^2 + b^2*c)*(d*x^(1/3) + c)^3 - 150*(2*a*b*c^3 + 3*b^2*c^2)*(d*x^(1/3) + c)^2 + 150*(a*b*c^4 + 2*b^2*c^3)*(d*x^(1/3) + c))*cos(2*d*x^(1/3) + 2*c) + (192*I*(d*x^(1/3) + c)^5*a*b - 150*I*b^2*c^4 + (-600*I*a*b*c - 300*I*b^2)*(d*x^(1/3) + c)^4 + (800*I*a*b*c^2 + 800*I*b^2*c)*(d*x^(1/3) + c)^3 + (-600*I*a*b*c^3 - 900*I*b^2*c^2)*(d*x^(1/3) + c)^2 + (300*I*a*b*c^4 + 600*I*b^2*c^3)*(d*x^(1/3) + c))*sin(2*d*x^(1/3) + 2*c))*arctan2(sin(2*d*x^(1/3) + 2*c), cos(2*d*x^(1/3) + 2*c) + 1) - 5*((2*a*b + I*b^2)*(d*x^(1/3) + c)^6 - 6*(2*b^2 + (2*a*b + I*b^2)*c)*(d*x^(1/3) + c)^5 + 15*(4*b^2*c + (2*a*b + I*b^2)*c^2)*(d*x^(1/3) + c)^4 - 20*(6*b^2*c^2 + (2*a*b + I*b^2)*c^3)*(d*x^(1/3) + c)^3 + 15*(8*b^2*c^3 + (2*a*b + I*b^2)*c^4)*(d*x^(1/3) + c)^2 + 6*(-I*b^2*c^5 - 10*b^2*c^4)*(d*x^(1/3) + c))*cos(2*d*x^(1/3) + 2*c) - (480*(d*x^(1/3) + c)^4*a*b + 150*a*b*c^4 + 300*b^2*c^3 - 600*(2*a*b*c + b^2)*(d*x^(1/3) + c)^3 + 1200*(a*b*c^2 + b^2*c)*(d*x^(1/3) + c)^2 - 300*(2*a*b*c^3 + 3*b^2*c^2)*(d*x^(1/3) + c) + 30*(16*(d*x^(1/3) + c)^4*a*b + 5*a*b*c^4 + 10*b^2*c^3 - 20*(2*a*b*c + b^2)*(d*x^(1/3) + c)^3 + 40*(a*b*c^2 + b^2*c)*(d*x^(1/3) + c)^2 - 10*(2*a*b*c^3 + 3*b^2*c^2)*(d*x^(1/3) + c))*cos(2*d*x^(1/3) + 2*c) - (-480*I*(d*x^(1/3) + c)^4*a*b - 150*I*a*b*c^4 - 300*I*b^2*c^3 + (1200*I*a*b*c + 600*I*b^2)*(d*x^(1/3) + c)^3 + (-1200*I*a*b*c^2 - 1200*I*b^2*c)*(d*x^(1/3) + c)^2 + (600*I*a*b*c^3 + 900*I*b^2*c^2)*(d*x^(1/3) + c))*sin(2*d*x^(1/3) + 2*c))*dilog(-e^(2*I*d*x^(1/3) + 2*I*c)) + (-96*I*(d*x^(1/3) + c)^5*a*b + 75*I*b^2*c^4 + (300*I*a*b*c + 150*I*b^2)*(d*x^(1/3) + c)^4 + (-400*I*a*b*c^2 - 400*I*b^2*c)*(d*x^(1/3) + c)^3 + (300*I*a*b*c^3 + 450*I*b^2*c^2)*(d*x^(1/3) + c)^2 + (-150*I*a*b*c^4 - 300*I*b^2*c^3)*(d*x^(1/3) + c) + (-96*I*(d*x^(1/3) + c)^5*a*b + 75*I*b^2*c^4 + (300*I*a*b*c + 150*I*b^2)*(d*x^(1/3) + c)^4 + (-400*I*a*b*c^2 - 400*I*b^2*c)*(d*x^(1/3) + c)^3 + (300*I*a*b*c^3 + 450*I*b^2*c^2)*(d*x^(1/3) + c)^2 + (-150*I*a*b*c^4 - 300*I*b^2*c^3)*(d*x^(1/3) + c))*cos(2*d*x^(1/3) + 2*c) + (96*(d*x^(1/3) + c)^5*a*b - 75*b^2*c^4 - 150*(2*a*b*c + b^2)*(d*x^(1/3) + c)^4 + 400*(a*b*c^2 + b^2*c)*(d*x^(1/3) + c)^3 - 150*(2*a*b*c^3 + 3*b^2*c^2)*(d*x^(1/3) + c)^2 + 150*(a*b*c^4 + 2*b^2*c^3)*(d*x^(1/3) + c))*sin(2*d*x^(1/3) + 2*c))*log(cos(2*d*x^(1/3) + 2*c)^2 + sin(2*d*x^(1/3) + 2*c)^2 + 2*cos(2*d*x^(1/3) + 2*c) + 1) - (720*a*b*cos(2*d*x^(1/3) + 2*c) + 720*I*a*b*sin(2*d*x^(1/3) + 2*c) + 720*a*b)*polylog(6, -e^(2*I*d*x^(1/3) + 2*I*c)) + (1440*I*(d*x^(1/3) + c)*a*b - 900*I*a*b*c - 450*I*b^2 + (1440*I*(d*x^(1/3) + c)*a*b - 900*I*a*b*c - 450*I*b^2)*cos(2*d*x^(1/3) + 2*c) - 90*(16*(d*x^(1/3) + c)*a*b - 10*a*b*c - 5*b^2)*sin(2*d*x^(1/3) + 2*c))*polylog(5, -e^(2*I*d*x^(1/3) + 2*I*c)) + (1440*(d*x^(1/3) + c)^2*a*b + 600*a*b*c^2 + 600*b^2*c - 900*(2*a*b*c + b^2)*(d*x^(1/3) + c) + 60*(24*(d*x^(1/3) + c)^2*a*b + 10*a*b*c^2 + 10*b^2*c - 15*(2*a*b*c + b^2)*(d*x^(1/3) + c))*cos(2*d*x^(1/3) + 2*c) + (1440*I*(d*x^(1/3) + c)^2*a*b + 600*I*a*b*c^2 + 600*I*b^2*c + (-1800*I*a*b*c - 900*I*b^2)*(d*x^(1/3) + c))*sin(2*d*x^(1/3) + 2*c))*polylog(4, -e^(2*I*d*x^(1/3) + 2*I*c)) + (-960*I*(d*x^(1/3) + c)^3*a*b + 300*I*a*b*c^3 + 450*I*b^2*c^2 + (1800*I*a*b*c + 900*I*b^2)*(d*x^(1/3) + c)^2 + (-1200*I*a*b*c^2 - 1200*I*b^2*c)*(d*x^(1/3) + c) + (-960*I*(d*x^(1/3) + c)^3*a*b + 300*I*a*b*c^3 + 450*I*b^2*c^2 + (1800*I*a*b*c + 900*I*b^2)*(d*x^(1/3) + c)^2 + (-1200*I*a*b*c^2 - 1200*I*b^2*c)*(d*x^(1/3) + c))*cos(2*d*x^(1/3) + 2*c) + 30*(32*(d*x^(1/3) + c)^3*a*b - 10*a*b*c^3 - 15*b^2*c^2 - 30*(2*a*b*c + b^2)*(d*x^(1/3) + c)^2 + 40*(a*b*c^2 + b^2*c)*(d*x^(1/3) + c))*sin(2*d*x^(1/3) + 2*c))*polylog(3, -e^(2*I*d*x^(1/3) + 2*I*c)) + ((-10*I*a*b + 5*b^2)*(d*x^(1/3) + c)^6 + (60*I*b^2 + (60*I*a*b - 30*b^2)*c)*(d*x^(1/3) + c)^5 + (-300*I*b^2*c + (-150*I*a*b + 75*b^2)*c^2)*(d*x^(1/3) + c)^4 + (600*I*b^2*c^2 + (200*I*a*b - 100*b^2)*c^3)*(d*x^(1/3) + c)^3 + (-600*I*b^2*c^3 + (-150*I*a*b + 75*b^2)*c^4)*(d*x^(1/3) + c)^2 - (30*b^2*c^5 - 300*I*b^2*c^4)*(d*x^(1/3) + c))*sin(2*d*x^(1/3) + 2*c))/(-30*I*cos(2*d*x^(1/3) + 2*c) + 30*sin(2*d*x^(1/3) + 2*c) - 30*I))/d^6","B",0
54,0,0,0,0.000000," ","integrate((a+b*tan(c+d*x^(1/3)))^2,x, algorithm=""maxima"")","a^{2} x + \frac{6 \, b^{2} x^{\frac{2}{3}} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - {\left(b^{2} d \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + b^{2} d \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + 2 \, b^{2} d \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + b^{2} d\right)} x - \frac{{\left(-8 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} a b + 4 \, {\left(6 i \, a b c + 3 i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + 12 \, a b {\rm Li}_{3}(-e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}) + 2 \, {\left(-12 i \, a b c^{2} - 12 i \, b^{2} c\right)} {\left(d x^{\frac{1}{3}} + c\right)} + {\left(24 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} a b + 24 i \, a b c^{2} + 24 i \, b^{2} c + 2 \, {\left(-24 i \, a b c - 12 i \, b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \arctan\left(\sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right), \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 1\right) + {\left(-24 i \, {\left(d x^{\frac{1}{3}} + c\right)} a b + 24 i \, a b c + 12 i \, b^{2}\right)} {\rm Li}_2\left(-e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}\right) + 12 \, {\left({\left(d x^{\frac{1}{3}} + c\right)}^{2} a b + a b c^{2} + b^{2} c - {\left(2 \, a b c + b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \log\left(\cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 1\right)\right)} {\left(d \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + d \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + d\right)}}{4 \, d^{3}}}{d \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + d \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + d}"," ",0,"a^2*x + (6*b^2*x^(2/3)*sin(2*d*x^(1/3) + 2*c) - (b^2*d*cos(2*d*x^(1/3) + 2*c)^2 + b^2*d*sin(2*d*x^(1/3) + 2*c)^2 + 2*b^2*d*cos(2*d*x^(1/3) + 2*c) + b^2*d)*x - (d*cos(2*d*x^(1/3) + 2*c)^2 + d*sin(2*d*x^(1/3) + 2*c)^2 + 2*d*cos(2*d*x^(1/3) + 2*c) + d)*integrate(-4*(a*b*d*x*sin(2*d*x^(1/3) + 2*c) - b^2*x^(2/3)*sin(2*d*x^(1/3) + 2*c))/((d*cos(2*d*x^(1/3) + 2*c)^2 + d*sin(2*d*x^(1/3) + 2*c)^2 + 2*d*cos(2*d*x^(1/3) + 2*c) + d)*x), x))/(d*cos(2*d*x^(1/3) + 2*c)^2 + d*sin(2*d*x^(1/3) + 2*c)^2 + 2*d*cos(2*d*x^(1/3) + 2*c) + d)","F",0
55,0,0,0,0.000000," ","integrate((a+b*tan(c+d*x^(1/3)))^2/x,x, algorithm=""maxima"")","\frac{6 \, b^{2} x^{\frac{2}{3}} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 2 \, {\left(d \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + d \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + d\right)} x \int \frac{2 \, a b d x \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + b^{2} x^{\frac{2}{3}} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)}{{\left(d \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + d \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + d\right)} x^{2}}\,{d x} + {\left({\left(a^{2} - b^{2}\right)} d \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + {\left(a^{2} - b^{2}\right)} d \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + 2 \, {\left(a^{2} - b^{2}\right)} d \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left(a^{2} - b^{2}\right)} d\right)} x \log\left(x\right)}{{\left(d \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + d \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + d\right)} x}"," ",0,"(6*b^2*x^(2/3)*sin(2*d*x^(1/3) + 2*c) + (d*cos(2*d*x^(1/3) + 2*c)^2 + d*sin(2*d*x^(1/3) + 2*c)^2 + 2*d*cos(2*d*x^(1/3) + 2*c) + d)*x*integrate(2*(2*a*b*d*x*sin(2*d*x^(1/3) + 2*c) + b^2*x^(2/3)*sin(2*d*x^(1/3) + 2*c))/((d*cos(2*d*x^(1/3) + 2*c)^2 + d*sin(2*d*x^(1/3) + 2*c)^2 + 2*d*cos(2*d*x^(1/3) + 2*c) + d)*x^2), x) + ((a^2 - b^2)*d*cos(2*d*x^(1/3) + 2*c)^2 + (a^2 - b^2)*d*sin(2*d*x^(1/3) + 2*c)^2 + 2*(a^2 - b^2)*d*cos(2*d*x^(1/3) + 2*c) + (a^2 - b^2)*d)*x*log(x))/((d*cos(2*d*x^(1/3) + 2*c)^2 + d*sin(2*d*x^(1/3) + 2*c)^2 + 2*d*cos(2*d*x^(1/3) + 2*c) + d)*x)","F",0
56,0,0,0,0.000000," ","integrate((a+b*tan(c+d*x^(1/3)))^2/x^2,x, algorithm=""maxima"")","\frac{4 \, {\left(d \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + d \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + d\right)} x^{2} \int \frac{a b d x \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 2 \, b^{2} x^{\frac{2}{3}} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)}{{\left(d \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + d \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + d\right)} x^{3}}\,{d x} + 6 \, b^{2} x^{\frac{2}{3}} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - {\left({\left(a^{2} - b^{2}\right)} d \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + {\left(a^{2} - b^{2}\right)} d \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + 2 \, {\left(a^{2} - b^{2}\right)} d \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left(a^{2} - b^{2}\right)} d\right)} x}{{\left(d \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + d \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + d\right)} x^{2}}"," ",0,"((d*cos(2*d*x^(1/3) + 2*c)^2 + d*sin(2*d*x^(1/3) + 2*c)^2 + 2*d*cos(2*d*x^(1/3) + 2*c) + d)*x^2*integrate(4*(a*b*d*x*sin(2*d*x^(1/3) + 2*c) + 2*b^2*x^(2/3)*sin(2*d*x^(1/3) + 2*c))/((d*cos(2*d*x^(1/3) + 2*c)^2 + d*sin(2*d*x^(1/3) + 2*c)^2 + 2*d*cos(2*d*x^(1/3) + 2*c) + d)*x^3), x) + 6*b^2*x^(2/3)*sin(2*d*x^(1/3) + 2*c) - ((a^2 - b^2)*d*cos(2*d*x^(1/3) + 2*c)^2 + (a^2 - b^2)*d*sin(2*d*x^(1/3) + 2*c)^2 + 2*(a^2 - b^2)*d*cos(2*d*x^(1/3) + 2*c) + (a^2 - b^2)*d)*x)/((d*cos(2*d*x^(1/3) + 2*c)^2 + d*sin(2*d*x^(1/3) + 2*c)^2 + 2*d*cos(2*d*x^(1/3) + 2*c) + d)*x^2)","F",0
57,1,1310,0,1.358255," ","integrate(x^2/(a+b*tan(c+d*x^(1/3))),x, algorithm=""maxima"")","\frac{315 \, {\left(\frac{2 \, {\left(d x^{\frac{1}{3}} + c\right)} a}{a^{2} + b^{2}} + \frac{2 \, b \log\left(b \tan\left(d x^{\frac{1}{3}} + c\right) + a\right)}{a^{2} + b^{2}} - \frac{b \log\left(\tan\left(d x^{\frac{1}{3}} + c\right)^{2} + 1\right)}{a^{2} + b^{2}}\right)} c^{8} + \frac{2 \, {\left(35 \, {\left(d x^{\frac{1}{3}} + c\right)}^{9} {\left(a - i \, b\right)} - 315 \, {\left(d x^{\frac{1}{3}} + c\right)}^{8} {\left(a - i \, b\right)} c + 1260 \, {\left(d x^{\frac{1}{3}} + c\right)}^{7} {\left(a - i \, b\right)} c^{2} - 2940 \, {\left(d x^{\frac{1}{3}} + c\right)}^{6} {\left(a - i \, b\right)} c^{3} + 4410 \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} {\left(a - i \, b\right)} c^{4} - 4410 \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} {\left(a - i \, b\right)} c^{5} + 2940 \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} {\left(a - i \, b\right)} c^{6} - 1260 \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} {\left(a - i \, b\right)} c^{7} + {\left(-5040 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{8} b + 23040 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{7} b c - 47040 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{6} b c^{2} + 56448 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} b c^{3} - 44100 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} b c^{4} + 23520 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} b c^{5} - 8820 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} b c^{6} + 2520 i \, {\left(d x^{\frac{1}{3}} + c\right)} b c^{7}\right)} \arctan\left(\frac{2 \, a b \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - {\left(a^{2} - b^{2}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)}{a^{2} + b^{2}}, \frac{2 \, a b \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + a^{2} + b^{2} + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)}{a^{2} + b^{2}}\right) + {\left(-20160 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{7} b + 80640 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{6} b c - 141120 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} b c^{2} + 141120 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} b c^{3} - 88200 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} b c^{4} + 35280 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} b c^{5} - 8820 i \, {\left(d x^{\frac{1}{3}} + c\right)} b c^{6} + 1260 i \, b c^{7}\right)} {\rm Li}_2\left(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}}{-i \, a + b}\right) + 6 \, {\left(420 \, {\left(d x^{\frac{1}{3}} + c\right)}^{8} b - 1920 \, {\left(d x^{\frac{1}{3}} + c\right)}^{7} b c + 3920 \, {\left(d x^{\frac{1}{3}} + c\right)}^{6} b c^{2} - 4704 \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} b c^{3} + 3675 \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} b c^{4} - 1960 \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} b c^{5} + 735 \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} b c^{6} - 210 \, {\left(d x^{\frac{1}{3}} + c\right)} b c^{7}\right)} \log\left(\frac{{\left(a^{2} + b^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + 4 \, a b \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)}{a^{2} + b^{2}}\right) - 793800 \, b {\rm Li}_{9}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}}{-i \, a + b}) + {\left(1587600 i \, {\left(d x^{\frac{1}{3}} + c\right)} b - 907200 i \, b c\right)} {\rm Li}_{8}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}}{-i \, a + b}) + 75600 \, {\left(21 \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} b - 24 \, {\left(d x^{\frac{1}{3}} + c\right)} b c + 7 \, b c^{2}\right)} {\rm Li}_{7}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}}{-i \, a + b}) + {\left(-1058400 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} b + 1814400 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} b c - 1058400 i \, {\left(d x^{\frac{1}{3}} + c\right)} b c^{2} + 211680 i \, b c^{3}\right)} {\rm Li}_{6}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}}{-i \, a + b}) - 1890 \, {\left(280 \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} b - 640 \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} b c + 560 \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} b c^{2} - 224 \, {\left(d x^{\frac{1}{3}} + c\right)} b c^{3} + 35 \, b c^{4}\right)} {\rm Li}_{5}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}}{-i \, a + b}) + {\left(211680 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} b - 604800 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} b c + 705600 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} b c^{2} - 423360 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} b c^{3} + 132300 i \, {\left(d x^{\frac{1}{3}} + c\right)} b c^{4} - 17640 i \, b c^{5}\right)} {\rm Li}_{4}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}}{-i \, a + b}) + 630 \, {\left(112 \, {\left(d x^{\frac{1}{3}} + c\right)}^{6} b - 384 \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} b c + 560 \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} b c^{2} - 448 \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} b c^{3} + 210 \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} b c^{4} - 56 \, {\left(d x^{\frac{1}{3}} + c\right)} b c^{5} + 7 \, b c^{6}\right)} {\rm Li}_{3}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}}{-i \, a + b})\right)}}{a^{2} + b^{2}}}{210 \, d^{9}}"," ",0,"1/210*(315*(2*(d*x^(1/3) + c)*a/(a^2 + b^2) + 2*b*log(b*tan(d*x^(1/3) + c) + a)/(a^2 + b^2) - b*log(tan(d*x^(1/3) + c)^2 + 1)/(a^2 + b^2))*c^8 + 2*(35*(d*x^(1/3) + c)^9*(a - I*b) - 315*(d*x^(1/3) + c)^8*(a - I*b)*c + 1260*(d*x^(1/3) + c)^7*(a - I*b)*c^2 - 2940*(d*x^(1/3) + c)^6*(a - I*b)*c^3 + 4410*(d*x^(1/3) + c)^5*(a - I*b)*c^4 - 4410*(d*x^(1/3) + c)^4*(a - I*b)*c^5 + 2940*(d*x^(1/3) + c)^3*(a - I*b)*c^6 - 1260*(d*x^(1/3) + c)^2*(a - I*b)*c^7 + (-5040*I*(d*x^(1/3) + c)^8*b + 23040*I*(d*x^(1/3) + c)^7*b*c - 47040*I*(d*x^(1/3) + c)^6*b*c^2 + 56448*I*(d*x^(1/3) + c)^5*b*c^3 - 44100*I*(d*x^(1/3) + c)^4*b*c^4 + 23520*I*(d*x^(1/3) + c)^3*b*c^5 - 8820*I*(d*x^(1/3) + c)^2*b*c^6 + 2520*I*(d*x^(1/3) + c)*b*c^7)*arctan2((2*a*b*cos(2*d*x^(1/3) + 2*c) - (a^2 - b^2)*sin(2*d*x^(1/3) + 2*c))/(a^2 + b^2), (2*a*b*sin(2*d*x^(1/3) + 2*c) + a^2 + b^2 + (a^2 - b^2)*cos(2*d*x^(1/3) + 2*c))/(a^2 + b^2)) + (-20160*I*(d*x^(1/3) + c)^7*b + 80640*I*(d*x^(1/3) + c)^6*b*c - 141120*I*(d*x^(1/3) + c)^5*b*c^2 + 141120*I*(d*x^(1/3) + c)^4*b*c^3 - 88200*I*(d*x^(1/3) + c)^3*b*c^4 + 35280*I*(d*x^(1/3) + c)^2*b*c^5 - 8820*I*(d*x^(1/3) + c)*b*c^6 + 1260*I*b*c^7)*dilog((I*a + b)*e^(2*I*d*x^(1/3) + 2*I*c)/(-I*a + b)) + 6*(420*(d*x^(1/3) + c)^8*b - 1920*(d*x^(1/3) + c)^7*b*c + 3920*(d*x^(1/3) + c)^6*b*c^2 - 4704*(d*x^(1/3) + c)^5*b*c^3 + 3675*(d*x^(1/3) + c)^4*b*c^4 - 1960*(d*x^(1/3) + c)^3*b*c^5 + 735*(d*x^(1/3) + c)^2*b*c^6 - 210*(d*x^(1/3) + c)*b*c^7)*log(((a^2 + b^2)*cos(2*d*x^(1/3) + 2*c)^2 + 4*a*b*sin(2*d*x^(1/3) + 2*c) + (a^2 + b^2)*sin(2*d*x^(1/3) + 2*c)^2 + a^2 + b^2 + 2*(a^2 - b^2)*cos(2*d*x^(1/3) + 2*c))/(a^2 + b^2)) - 793800*b*polylog(9, (I*a + b)*e^(2*I*d*x^(1/3) + 2*I*c)/(-I*a + b)) + (1587600*I*(d*x^(1/3) + c)*b - 907200*I*b*c)*polylog(8, (I*a + b)*e^(2*I*d*x^(1/3) + 2*I*c)/(-I*a + b)) + 75600*(21*(d*x^(1/3) + c)^2*b - 24*(d*x^(1/3) + c)*b*c + 7*b*c^2)*polylog(7, (I*a + b)*e^(2*I*d*x^(1/3) + 2*I*c)/(-I*a + b)) + (-1058400*I*(d*x^(1/3) + c)^3*b + 1814400*I*(d*x^(1/3) + c)^2*b*c - 1058400*I*(d*x^(1/3) + c)*b*c^2 + 211680*I*b*c^3)*polylog(6, (I*a + b)*e^(2*I*d*x^(1/3) + 2*I*c)/(-I*a + b)) - 1890*(280*(d*x^(1/3) + c)^4*b - 640*(d*x^(1/3) + c)^3*b*c + 560*(d*x^(1/3) + c)^2*b*c^2 - 224*(d*x^(1/3) + c)*b*c^3 + 35*b*c^4)*polylog(5, (I*a + b)*e^(2*I*d*x^(1/3) + 2*I*c)/(-I*a + b)) + (211680*I*(d*x^(1/3) + c)^5*b - 604800*I*(d*x^(1/3) + c)^4*b*c + 705600*I*(d*x^(1/3) + c)^3*b*c^2 - 423360*I*(d*x^(1/3) + c)^2*b*c^3 + 132300*I*(d*x^(1/3) + c)*b*c^4 - 17640*I*b*c^5)*polylog(4, (I*a + b)*e^(2*I*d*x^(1/3) + 2*I*c)/(-I*a + b)) + 630*(112*(d*x^(1/3) + c)^6*b - 384*(d*x^(1/3) + c)^5*b*c + 560*(d*x^(1/3) + c)^4*b*c^2 - 448*(d*x^(1/3) + c)^3*b*c^3 + 210*(d*x^(1/3) + c)^2*b*c^4 - 56*(d*x^(1/3) + c)*b*c^5 + 7*b*c^6)*polylog(3, (I*a + b)*e^(2*I*d*x^(1/3) + 2*I*c)/(-I*a + b)))/(a^2 + b^2))/d^9","B",0
58,1,810,0,1.319499," ","integrate(x/(a+b*tan(c+d*x^(1/3))),x, algorithm=""maxima"")","-\frac{15 \, {\left(\frac{2 \, {\left(d x^{\frac{1}{3}} + c\right)} a}{a^{2} + b^{2}} + \frac{2 \, b \log\left(b \tan\left(d x^{\frac{1}{3}} + c\right) + a\right)}{a^{2} + b^{2}} - \frac{b \log\left(\tan\left(d x^{\frac{1}{3}} + c\right)^{2} + 1\right)}{a^{2} + b^{2}}\right)} c^{5} - \frac{5 \, {\left(d x^{\frac{1}{3}} + c\right)}^{6} {\left(a - i \, b\right)} - 30 \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} {\left(a - i \, b\right)} c + 75 \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} {\left(a - i \, b\right)} c^{2} - 100 \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} {\left(a - i \, b\right)} c^{3} + 75 \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} {\left(a - i \, b\right)} c^{4} + {\left(-96 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} b + 300 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} b c - 400 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} b c^{2} + 300 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} b c^{3} - 150 i \, {\left(d x^{\frac{1}{3}} + c\right)} b c^{4}\right)} \arctan\left(\frac{2 \, a b \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - {\left(a^{2} - b^{2}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)}{a^{2} + b^{2}}, \frac{2 \, a b \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + a^{2} + b^{2} + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)}{a^{2} + b^{2}}\right) + {\left(-240 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} b + 600 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} b c - 600 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} b c^{2} + 300 i \, {\left(d x^{\frac{1}{3}} + c\right)} b c^{3} - 75 i \, b c^{4}\right)} {\rm Li}_2\left(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}}{-i \, a + b}\right) + {\left(48 \, {\left(d x^{\frac{1}{3}} + c\right)}^{5} b - 150 \, {\left(d x^{\frac{1}{3}} + c\right)}^{4} b c + 200 \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} b c^{2} - 150 \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} b c^{3} + 75 \, {\left(d x^{\frac{1}{3}} + c\right)} b c^{4}\right)} \log\left(\frac{{\left(a^{2} + b^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + 4 \, a b \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)}{a^{2} + b^{2}}\right) - 360 i \, b {\rm Li}_{6}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}}{-i \, a + b}) - 90 \, {\left(8 \, {\left(d x^{\frac{1}{3}} + c\right)} b - 5 \, b c\right)} {\rm Li}_{5}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}}{-i \, a + b}) + {\left(720 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} b - 900 i \, {\left(d x^{\frac{1}{3}} + c\right)} b c + 300 i \, b c^{2}\right)} {\rm Li}_{4}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}}{-i \, a + b}) + 30 \, {\left(16 \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} b - 30 \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} b c + 20 \, {\left(d x^{\frac{1}{3}} + c\right)} b c^{2} - 5 \, b c^{3}\right)} {\rm Li}_{3}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}}{-i \, a + b})}{a^{2} + b^{2}}}{10 \, d^{6}}"," ",0,"-1/10*(15*(2*(d*x^(1/3) + c)*a/(a^2 + b^2) + 2*b*log(b*tan(d*x^(1/3) + c) + a)/(a^2 + b^2) - b*log(tan(d*x^(1/3) + c)^2 + 1)/(a^2 + b^2))*c^5 - (5*(d*x^(1/3) + c)^6*(a - I*b) - 30*(d*x^(1/3) + c)^5*(a - I*b)*c + 75*(d*x^(1/3) + c)^4*(a - I*b)*c^2 - 100*(d*x^(1/3) + c)^3*(a - I*b)*c^3 + 75*(d*x^(1/3) + c)^2*(a - I*b)*c^4 + (-96*I*(d*x^(1/3) + c)^5*b + 300*I*(d*x^(1/3) + c)^4*b*c - 400*I*(d*x^(1/3) + c)^3*b*c^2 + 300*I*(d*x^(1/3) + c)^2*b*c^3 - 150*I*(d*x^(1/3) + c)*b*c^4)*arctan2((2*a*b*cos(2*d*x^(1/3) + 2*c) - (a^2 - b^2)*sin(2*d*x^(1/3) + 2*c))/(a^2 + b^2), (2*a*b*sin(2*d*x^(1/3) + 2*c) + a^2 + b^2 + (a^2 - b^2)*cos(2*d*x^(1/3) + 2*c))/(a^2 + b^2)) + (-240*I*(d*x^(1/3) + c)^4*b + 600*I*(d*x^(1/3) + c)^3*b*c - 600*I*(d*x^(1/3) + c)^2*b*c^2 + 300*I*(d*x^(1/3) + c)*b*c^3 - 75*I*b*c^4)*dilog((I*a + b)*e^(2*I*d*x^(1/3) + 2*I*c)/(-I*a + b)) + (48*(d*x^(1/3) + c)^5*b - 150*(d*x^(1/3) + c)^4*b*c + 200*(d*x^(1/3) + c)^3*b*c^2 - 150*(d*x^(1/3) + c)^2*b*c^3 + 75*(d*x^(1/3) + c)*b*c^4)*log(((a^2 + b^2)*cos(2*d*x^(1/3) + 2*c)^2 + 4*a*b*sin(2*d*x^(1/3) + 2*c) + (a^2 + b^2)*sin(2*d*x^(1/3) + 2*c)^2 + a^2 + b^2 + 2*(a^2 - b^2)*cos(2*d*x^(1/3) + 2*c))/(a^2 + b^2)) - 360*I*b*polylog(6, (I*a + b)*e^(2*I*d*x^(1/3) + 2*I*c)/(-I*a + b)) - 90*(8*(d*x^(1/3) + c)*b - 5*b*c)*polylog(5, (I*a + b)*e^(2*I*d*x^(1/3) + 2*I*c)/(-I*a + b)) + (720*I*(d*x^(1/3) + c)^2*b - 900*I*(d*x^(1/3) + c)*b*c + 300*I*b*c^2)*polylog(4, (I*a + b)*e^(2*I*d*x^(1/3) + 2*I*c)/(-I*a + b)) + 30*(16*(d*x^(1/3) + c)^3*b - 30*(d*x^(1/3) + c)^2*b*c + 20*(d*x^(1/3) + c)*b*c^2 - 5*b*c^3)*polylog(3, (I*a + b)*e^(2*I*d*x^(1/3) + 2*I*c)/(-I*a + b)))/(a^2 + b^2))/d^6","B",0
59,1,444,0,1.093839," ","integrate(1/(a+b*tan(c+d*x^(1/3))),x, algorithm=""maxima"")","\frac{3 \, {\left(\frac{2 \, {\left(d x^{\frac{1}{3}} + c\right)} a}{a^{2} + b^{2}} + \frac{2 \, b \log\left(b \tan\left(d x^{\frac{1}{3}} + c\right) + a\right)}{a^{2} + b^{2}} - \frac{b \log\left(\tan\left(d x^{\frac{1}{3}} + c\right)^{2} + 1\right)}{a^{2} + b^{2}}\right)} c^{2} + \frac{2 \, {\left(d x^{\frac{1}{3}} + c\right)}^{3} {\left(a - i \, b\right)} - 6 \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} {\left(a - i \, b\right)} c + {\left(-6 i \, {\left(d x^{\frac{1}{3}} + c\right)}^{2} b + 12 i \, {\left(d x^{\frac{1}{3}} + c\right)} b c\right)} \arctan\left(\frac{2 \, a b \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - {\left(a^{2} - b^{2}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)}{a^{2} + b^{2}}, \frac{2 \, a b \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + a^{2} + b^{2} + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)}{a^{2} + b^{2}}\right) + {\left(-6 i \, {\left(d x^{\frac{1}{3}} + c\right)} b + 6 i \, b c\right)} {\rm Li}_2\left(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}}{-i \, a + b}\right) + 3 \, {\left({\left(d x^{\frac{1}{3}} + c\right)}^{2} b - 2 \, {\left(d x^{\frac{1}{3}} + c\right)} b c\right)} \log\left(\frac{{\left(a^{2} + b^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + 4 \, a b \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)}{a^{2} + b^{2}}\right) + 3 \, b {\rm Li}_{3}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}}{-i \, a + b})}{a^{2} + b^{2}}}{2 \, d^{3}}"," ",0,"1/2*(3*(2*(d*x^(1/3) + c)*a/(a^2 + b^2) + 2*b*log(b*tan(d*x^(1/3) + c) + a)/(a^2 + b^2) - b*log(tan(d*x^(1/3) + c)^2 + 1)/(a^2 + b^2))*c^2 + (2*(d*x^(1/3) + c)^3*(a - I*b) - 6*(d*x^(1/3) + c)^2*(a - I*b)*c + (-6*I*(d*x^(1/3) + c)^2*b + 12*I*(d*x^(1/3) + c)*b*c)*arctan2((2*a*b*cos(2*d*x^(1/3) + 2*c) - (a^2 - b^2)*sin(2*d*x^(1/3) + 2*c))/(a^2 + b^2), (2*a*b*sin(2*d*x^(1/3) + 2*c) + a^2 + b^2 + (a^2 - b^2)*cos(2*d*x^(1/3) + 2*c))/(a^2 + b^2)) + (-6*I*(d*x^(1/3) + c)*b + 6*I*b*c)*dilog((I*a + b)*e^(2*I*d*x^(1/3) + 2*I*c)/(-I*a + b)) + 3*((d*x^(1/3) + c)^2*b - 2*(d*x^(1/3) + c)*b*c)*log(((a^2 + b^2)*cos(2*d*x^(1/3) + 2*c)^2 + 4*a*b*sin(2*d*x^(1/3) + 2*c) + (a^2 + b^2)*sin(2*d*x^(1/3) + 2*c)^2 + a^2 + b^2 + 2*(a^2 - b^2)*cos(2*d*x^(1/3) + 2*c))/(a^2 + b^2)) + 3*b*polylog(3, (I*a + b)*e^(2*I*d*x^(1/3) + 2*I*c)/(-I*a + b)))/(a^2 + b^2))/d^3","B",0
60,-1,0,0,0.000000," ","integrate(1/x/(a+b*tan(c+d*x^(1/3))),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
61,-1,0,0,0.000000," ","integrate(1/x^2/(a+b*tan(c+d*x^(1/3))),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
62,1,8147,0,5.429186," ","integrate(x^2/(a+b*tan(c+d*x^(1/3)))^2,x, algorithm=""maxima"")","\frac{3 \, {\left({\left(\frac{2 \, a b \log\left(b \tan\left(d x^{\frac{1}{3}} + c\right) + a\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{a b \log\left(\tan\left(d x^{\frac{1}{3}} + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(a^{2} - b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{b}{a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} \tan\left(d x^{\frac{1}{3}} + c\right)}\right)} c^{8} + \frac{{\left(35 \, a^{3} - 35 i \, a^{2} b + 35 \, a b^{2} - 35 i \, b^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{9} - {\left(315 \, a^{3} - 315 i \, a^{2} b + 315 \, a b^{2} - 315 i \, b^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{8} c + {\left(1260 \, a^{3} - 1260 i \, a^{2} b + 1260 \, a b^{2} - 1260 i \, b^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{7} c^{2} - {\left(2940 \, a^{3} - 2940 i \, a^{2} b + 2940 \, a b^{2} - 2940 i \, b^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} c^{3} + {\left(4410 \, a^{3} - 4410 i \, a^{2} b + 4410 \, a b^{2} - 4410 i \, b^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} c^{4} - {\left(4410 \, a^{3} - 4410 i \, a^{2} b + 4410 \, a b^{2} - 4410 i \, b^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} c^{5} + {\left(2940 \, a^{3} - 2940 i \, a^{2} b + 2940 \, a b^{2} - 2940 i \, b^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} c^{6} - {\left(1260 \, a^{3} - 1260 i \, a^{2} b + 1260 \, a b^{2} - 1260 i \, b^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} c^{7} + {\left({\left(-2520 i \, a b^{2} - 2520 \, b^{3}\right)} c^{7} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 2520 \, {\left(a b^{2} - i \, b^{3}\right)} c^{7} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left(-2520 i \, a b^{2} + 2520 \, b^{3}\right)} c^{7}\right)} \arctan\left(-b \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + a \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + b, a \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + b \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + a\right) + {\left({\left(-10080 i \, a^{2} b + 10080 \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{8} + {\left(-23040 i \, a b^{2} + 23040 \, b^{3} + {\left(46080 i \, a^{2} b - 46080 \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{7} + {\left({\left(-94080 i \, a^{2} b + 94080 \, a b^{2}\right)} c^{2} + {\left(94080 i \, a b^{2} - 94080 \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} + {\left({\left(112896 i \, a^{2} b - 112896 \, a b^{2}\right)} c^{3} + {\left(-169344 i \, a b^{2} + 169344 \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + {\left({\left(-88200 i \, a^{2} b + 88200 \, a b^{2}\right)} c^{4} + {\left(176400 i \, a b^{2} - 176400 \, b^{3}\right)} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + {\left({\left(47040 i \, a^{2} b - 47040 \, a b^{2}\right)} c^{5} + {\left(-117600 i \, a b^{2} + 117600 \, b^{3}\right)} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left({\left(-17640 i \, a^{2} b + 17640 \, a b^{2}\right)} c^{6} + {\left(52920 i \, a b^{2} - 52920 \, b^{3}\right)} c^{5}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left({\left(5040 i \, a^{2} b - 5040 \, a b^{2}\right)} c^{7} + {\left(-17640 i \, a b^{2} + 17640 \, b^{3}\right)} c^{6}\right)} {\left(d x^{\frac{1}{3}} + c\right)} + {\left({\left(-10080 i \, a^{2} b - 10080 \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{8} + {\left(-23040 i \, a b^{2} - 23040 \, b^{3} + {\left(46080 i \, a^{2} b + 46080 \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{7} + {\left({\left(-94080 i \, a^{2} b - 94080 \, a b^{2}\right)} c^{2} + {\left(94080 i \, a b^{2} + 94080 \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} + {\left({\left(112896 i \, a^{2} b + 112896 \, a b^{2}\right)} c^{3} + {\left(-169344 i \, a b^{2} - 169344 \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + {\left({\left(-88200 i \, a^{2} b - 88200 \, a b^{2}\right)} c^{4} + {\left(176400 i \, a b^{2} + 176400 \, b^{3}\right)} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + {\left({\left(47040 i \, a^{2} b + 47040 \, a b^{2}\right)} c^{5} + {\left(-117600 i \, a b^{2} - 117600 \, b^{3}\right)} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left({\left(-17640 i \, a^{2} b - 17640 \, a b^{2}\right)} c^{6} + {\left(52920 i \, a b^{2} + 52920 \, b^{3}\right)} c^{5}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left({\left(5040 i \, a^{2} b + 5040 \, a b^{2}\right)} c^{7} + {\left(-17640 i \, a b^{2} - 17640 \, b^{3}\right)} c^{6}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 24 \, {\left(420 \, {\left(a^{2} b - i \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{8} + 960 \, {\left(a b^{2} - i \, b^{3} - 2 \, {\left(a^{2} b - i \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{7} + 3920 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} c^{2} - {\left(a b^{2} - i \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} - 2352 \, {\left(2 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{3} - 3 \, {\left(a b^{2} - i \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + 3675 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} c^{4} - 2 \, {\left(a b^{2} - i \, b^{3}\right)} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} - 980 \, {\left(2 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{5} - 5 \, {\left(a b^{2} - i \, b^{3}\right)} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + 735 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} c^{6} - 3 \, {\left(a b^{2} - i \, b^{3}\right)} c^{5}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} - 105 \, {\left(2 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{7} - 7 \, {\left(a b^{2} - i \, b^{3}\right)} c^{6}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} \arctan\left(\frac{2 \, a b \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - {\left(a^{2} - b^{2}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)}{a^{2} + b^{2}}, \frac{2 \, a b \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + a^{2} + b^{2} + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)}{a^{2} + b^{2}}\right) + {\left({\left(35 \, a^{3} - 105 i \, a^{2} b - 105 \, a b^{2} + 35 i \, b^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{9} + {\left(-630 i \, a b^{2} - 630 \, b^{3} - {\left(315 \, a^{3} - 945 i \, a^{2} b - 945 \, a b^{2} + 315 i \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{8} + {\left(5040 i \, a b^{2} + 5040 \, b^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)} c^{7} + {\left({\left(1260 \, a^{3} - 3780 i \, a^{2} b - 3780 \, a b^{2} + 1260 i \, b^{3}\right)} c^{2} + {\left(5040 i \, a b^{2} + 5040 \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{7} - {\left({\left(2940 \, a^{3} - 8820 i \, a^{2} b - 8820 \, a b^{2} + 2940 i \, b^{3}\right)} c^{3} - {\left(-17640 i \, a b^{2} - 17640 \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} + {\left({\left(4410 \, a^{3} - 13230 i \, a^{2} b - 13230 \, a b^{2} + 4410 i \, b^{3}\right)} c^{4} + {\left(35280 i \, a b^{2} + 35280 \, b^{3}\right)} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} - {\left({\left(4410 \, a^{3} - 13230 i \, a^{2} b - 13230 \, a b^{2} + 4410 i \, b^{3}\right)} c^{5} - {\left(-44100 i \, a b^{2} - 44100 \, b^{3}\right)} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + {\left({\left(2940 \, a^{3} - 8820 i \, a^{2} b - 8820 \, a b^{2} + 2940 i \, b^{3}\right)} c^{6} + {\left(35280 i \, a b^{2} + 35280 \, b^{3}\right)} c^{5}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} - {\left({\left(1260 \, a^{3} - 3780 i \, a^{2} b - 3780 \, a b^{2} + 1260 i \, b^{3}\right)} c^{7} - {\left(-17640 i \, a b^{2} - 17640 \, b^{3}\right)} c^{6}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left({\left(-40320 i \, a^{2} b + 40320 \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{7} + {\left(2520 i \, a^{2} b - 2520 \, a b^{2}\right)} c^{7} + {\left(-80640 i \, a b^{2} + 80640 \, b^{3} + {\left(161280 i \, a^{2} b - 161280 \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} + {\left(-8820 i \, a b^{2} + 8820 \, b^{3}\right)} c^{6} + {\left({\left(-282240 i \, a^{2} b + 282240 \, a b^{2}\right)} c^{2} + {\left(282240 i \, a b^{2} - 282240 \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + {\left({\left(282240 i \, a^{2} b - 282240 \, a b^{2}\right)} c^{3} + {\left(-423360 i \, a b^{2} + 423360 \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + {\left({\left(-176400 i \, a^{2} b + 176400 \, a b^{2}\right)} c^{4} + {\left(352800 i \, a b^{2} - 352800 \, b^{3}\right)} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left({\left(70560 i \, a^{2} b - 70560 \, a b^{2}\right)} c^{5} + {\left(-176400 i \, a b^{2} + 176400 \, b^{3}\right)} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left({\left(-17640 i \, a^{2} b + 17640 \, a b^{2}\right)} c^{6} + {\left(52920 i \, a b^{2} - 52920 \, b^{3}\right)} c^{5}\right)} {\left(d x^{\frac{1}{3}} + c\right)} + {\left({\left(-40320 i \, a^{2} b - 40320 \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{7} + {\left(2520 i \, a^{2} b + 2520 \, a b^{2}\right)} c^{7} + {\left(-80640 i \, a b^{2} - 80640 \, b^{3} + {\left(161280 i \, a^{2} b + 161280 \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} + {\left(-8820 i \, a b^{2} - 8820 \, b^{3}\right)} c^{6} + {\left({\left(-282240 i \, a^{2} b - 282240 \, a b^{2}\right)} c^{2} + {\left(282240 i \, a b^{2} + 282240 \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + {\left({\left(282240 i \, a^{2} b + 282240 \, a b^{2}\right)} c^{3} + {\left(-423360 i \, a b^{2} - 423360 \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + {\left({\left(-176400 i \, a^{2} b - 176400 \, a b^{2}\right)} c^{4} + {\left(352800 i \, a b^{2} + 352800 \, b^{3}\right)} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left({\left(70560 i \, a^{2} b + 70560 \, a b^{2}\right)} c^{5} + {\left(-176400 i \, a b^{2} - 176400 \, b^{3}\right)} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left({\left(-17640 i \, a^{2} b - 17640 \, a b^{2}\right)} c^{6} + {\left(52920 i \, a b^{2} + 52920 \, b^{3}\right)} c^{5}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 1260 \, {\left(32 \, {\left(a^{2} b - i \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{7} - 2 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{7} + 64 \, {\left(a b^{2} - i \, b^{3} - 2 \, {\left(a^{2} b - i \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} + 7 \, {\left(a b^{2} - i \, b^{3}\right)} c^{6} + 224 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} c^{2} - {\left(a b^{2} - i \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} - 112 \, {\left(2 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{3} - 3 \, {\left(a b^{2} - i \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + 140 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} c^{4} - 2 \, {\left(a b^{2} - i \, b^{3}\right)} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} - 28 \, {\left(2 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{5} - 5 \, {\left(a b^{2} - i \, b^{3}\right)} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + 14 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} c^{6} - 3 \, {\left(a b^{2} - i \, b^{3}\right)} c^{5}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} {\rm Li}_2\left(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}}{-i \, a + b}\right) - {\left(1260 \, {\left(a b^{2} - i \, b^{3}\right)} c^{7} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - {\left(-1260 i \, a b^{2} - 1260 \, b^{3}\right)} c^{7} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 1260 \, {\left(a b^{2} + i \, b^{3}\right)} c^{7}\right)} \log\left({\left(a^{2} + b^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + 4 \, a b \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right) + {\left(5040 \, {\left(a^{2} b + i \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{8} + 11520 \, {\left(a b^{2} + i \, b^{3} - 2 \, {\left(a^{2} b + i \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{7} + 47040 \, {\left({\left(a^{2} b + i \, a b^{2}\right)} c^{2} - {\left(a b^{2} + i \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} - 28224 \, {\left(2 \, {\left(a^{2} b + i \, a b^{2}\right)} c^{3} - 3 \, {\left(a b^{2} + i \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + 44100 \, {\left({\left(a^{2} b + i \, a b^{2}\right)} c^{4} - 2 \, {\left(a b^{2} + i \, b^{3}\right)} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} - 11760 \, {\left(2 \, {\left(a^{2} b + i \, a b^{2}\right)} c^{5} - 5 \, {\left(a b^{2} + i \, b^{3}\right)} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + 8820 \, {\left({\left(a^{2} b + i \, a b^{2}\right)} c^{6} - 3 \, {\left(a b^{2} + i \, b^{3}\right)} c^{5}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} - 1260 \, {\left(2 \, {\left(a^{2} b + i \, a b^{2}\right)} c^{7} - 7 \, {\left(a b^{2} + i \, b^{3}\right)} c^{6}\right)} {\left(d x^{\frac{1}{3}} + c\right)} + 12 \, {\left(420 \, {\left(a^{2} b - i \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{8} + 960 \, {\left(a b^{2} - i \, b^{3} - 2 \, {\left(a^{2} b - i \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{7} + 3920 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} c^{2} - {\left(a b^{2} - i \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} - 2352 \, {\left(2 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{3} - 3 \, {\left(a b^{2} - i \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + 3675 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} c^{4} - 2 \, {\left(a b^{2} - i \, b^{3}\right)} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} - 980 \, {\left(2 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{5} - 5 \, {\left(a b^{2} - i \, b^{3}\right)} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + 735 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} c^{6} - 3 \, {\left(a b^{2} - i \, b^{3}\right)} c^{5}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} - 105 \, {\left(2 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{7} - 7 \, {\left(a b^{2} - i \, b^{3}\right)} c^{6}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left({\left(5040 i \, a^{2} b + 5040 \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{8} + {\left(11520 i \, a b^{2} + 11520 \, b^{3} + {\left(-23040 i \, a^{2} b - 23040 \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{7} + {\left({\left(47040 i \, a^{2} b + 47040 \, a b^{2}\right)} c^{2} + {\left(-47040 i \, a b^{2} - 47040 \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} + {\left({\left(-56448 i \, a^{2} b - 56448 \, a b^{2}\right)} c^{3} + {\left(84672 i \, a b^{2} + 84672 \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + {\left({\left(44100 i \, a^{2} b + 44100 \, a b^{2}\right)} c^{4} + {\left(-88200 i \, a b^{2} - 88200 \, b^{3}\right)} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + {\left({\left(-23520 i \, a^{2} b - 23520 \, a b^{2}\right)} c^{5} + {\left(58800 i \, a b^{2} + 58800 \, b^{3}\right)} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left({\left(8820 i \, a^{2} b + 8820 \, a b^{2}\right)} c^{6} + {\left(-26460 i \, a b^{2} - 26460 \, b^{3}\right)} c^{5}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left({\left(-2520 i \, a^{2} b - 2520 \, a b^{2}\right)} c^{7} + {\left(8820 i \, a b^{2} + 8820 \, b^{3}\right)} c^{6}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} \log\left(\frac{{\left(a^{2} + b^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + 4 \, a b \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)}{a^{2} + b^{2}}\right) - {\left(1587600 \, a^{2} b + 1587600 i \, a b^{2} + 1587600 \, {\left(a^{2} b - i \, a b^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - {\left(-1587600 i \, a^{2} b - 1587600 \, a b^{2}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} {\rm Li}_{9}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}}{-i \, a + b}) + {\left(907200 i \, a b^{2} - 907200 \, b^{3} + {\left(3175200 i \, a^{2} b - 3175200 \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)} + {\left(-1814400 i \, a^{2} b + 1814400 \, a b^{2}\right)} c + {\left(907200 i \, a b^{2} + 907200 \, b^{3} + {\left(3175200 i \, a^{2} b + 3175200 \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)} + {\left(-1814400 i \, a^{2} b - 1814400 \, a b^{2}\right)} c\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - 453600 \, {\left(2 \, a b^{2} - 2 i \, b^{3} + 7 \, {\left(a^{2} b - i \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)} - 4 \, {\left(a^{2} b - i \, a b^{2}\right)} c\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} {\rm Li}_{8}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}}{-i \, a + b}) + {\left(3175200 \, {\left(a^{2} b + i \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + 1058400 \, {\left(a^{2} b + i \, a b^{2}\right)} c^{2} + 1814400 \, {\left(a b^{2} + i \, b^{3} - 2 \, {\left(a^{2} b + i \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)} - 1058400 \, {\left(a b^{2} + i \, b^{3}\right)} c + 151200 \, {\left(21 \, {\left(a^{2} b - i \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + 7 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{2} + 12 \, {\left(a b^{2} - i \, b^{3} - 2 \, {\left(a^{2} b - i \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)} - 7 \, {\left(a b^{2} - i \, b^{3}\right)} c\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left({\left(3175200 i \, a^{2} b + 3175200 \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left(1058400 i \, a^{2} b + 1058400 \, a b^{2}\right)} c^{2} + {\left(1814400 i \, a b^{2} + 1814400 \, b^{3} + {\left(-3628800 i \, a^{2} b - 3628800 \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)} + {\left(-1058400 i \, a b^{2} - 1058400 \, b^{3}\right)} c\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} {\rm Li}_{7}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}}{-i \, a + b}) + {\left({\left(-2116800 i \, a^{2} b + 2116800 \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left(423360 i \, a^{2} b - 423360 \, a b^{2}\right)} c^{3} + {\left(-1814400 i \, a b^{2} + 1814400 \, b^{3} + {\left(3628800 i \, a^{2} b - 3628800 \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left(-635040 i \, a b^{2} + 635040 \, b^{3}\right)} c^{2} + {\left({\left(-2116800 i \, a^{2} b + 2116800 \, a b^{2}\right)} c^{2} + {\left(2116800 i \, a b^{2} - 2116800 \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)} + {\left({\left(-2116800 i \, a^{2} b - 2116800 \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left(423360 i \, a^{2} b + 423360 \, a b^{2}\right)} c^{3} + {\left(-1814400 i \, a b^{2} - 1814400 \, b^{3} + {\left(3628800 i \, a^{2} b + 3628800 \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left(-635040 i \, a b^{2} - 635040 \, b^{3}\right)} c^{2} + {\left({\left(-2116800 i \, a^{2} b - 2116800 \, a b^{2}\right)} c^{2} + {\left(2116800 i \, a b^{2} + 2116800 \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 30240 \, {\left(70 \, {\left(a^{2} b - i \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} - 14 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{3} + 60 \, {\left(a b^{2} - i \, b^{3} - 2 \, {\left(a^{2} b - i \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + 21 \, {\left(a b^{2} - i \, b^{3}\right)} c^{2} + 70 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} c^{2} - {\left(a b^{2} - i \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} {\rm Li}_{6}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}}{-i \, a + b}) - {\left(1058400 \, {\left(a^{2} b + i \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + 132300 \, {\left(a^{2} b + i \, a b^{2}\right)} c^{4} + 1209600 \, {\left(a b^{2} + i \, b^{3} - 2 \, {\left(a^{2} b + i \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} - 264600 \, {\left(a b^{2} + i \, b^{3}\right)} c^{3} + 2116800 \, {\left({\left(a^{2} b + i \, a b^{2}\right)} c^{2} - {\left(a b^{2} + i \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} - 423360 \, {\left(2 \, {\left(a^{2} b + i \, a b^{2}\right)} c^{3} - 3 \, {\left(a b^{2} + i \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)} + 3780 \, {\left(280 \, {\left(a^{2} b - i \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + 35 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{4} + 320 \, {\left(a b^{2} - i \, b^{3} - 2 \, {\left(a^{2} b - i \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} - 70 \, {\left(a b^{2} - i \, b^{3}\right)} c^{3} + 560 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} c^{2} - {\left(a b^{2} - i \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} - 112 \, {\left(2 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{3} - 3 \, {\left(a b^{2} - i \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - {\left({\left(-1058400 i \, a^{2} b - 1058400 \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + {\left(-132300 i \, a^{2} b - 132300 \, a b^{2}\right)} c^{4} + {\left(-1209600 i \, a b^{2} - 1209600 \, b^{3} + {\left(2419200 i \, a^{2} b + 2419200 \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left(264600 i \, a b^{2} + 264600 \, b^{3}\right)} c^{3} + {\left({\left(-2116800 i \, a^{2} b - 2116800 \, a b^{2}\right)} c^{2} + {\left(2116800 i \, a b^{2} + 2116800 \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left({\left(846720 i \, a^{2} b + 846720 \, a b^{2}\right)} c^{3} + {\left(-1270080 i \, a b^{2} - 1270080 \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} {\rm Li}_{5}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}}{-i \, a + b}) + {\left({\left(423360 i \, a^{2} b - 423360 \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + {\left(-35280 i \, a^{2} b + 35280 \, a b^{2}\right)} c^{5} + {\left(604800 i \, a b^{2} - 604800 \, b^{3} + {\left(-1209600 i \, a^{2} b + 1209600 \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + {\left(88200 i \, a b^{2} - 88200 \, b^{3}\right)} c^{4} + {\left({\left(1411200 i \, a^{2} b - 1411200 \, a b^{2}\right)} c^{2} + {\left(-1411200 i \, a b^{2} + 1411200 \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left({\left(-846720 i \, a^{2} b + 846720 \, a b^{2}\right)} c^{3} + {\left(1270080 i \, a b^{2} - 1270080 \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left({\left(264600 i \, a^{2} b - 264600 \, a b^{2}\right)} c^{4} + {\left(-529200 i \, a b^{2} + 529200 \, b^{3}\right)} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)} + {\left({\left(423360 i \, a^{2} b + 423360 \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + {\left(-35280 i \, a^{2} b - 35280 \, a b^{2}\right)} c^{5} + {\left(604800 i \, a b^{2} + 604800 \, b^{3} + {\left(-1209600 i \, a^{2} b - 1209600 \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + {\left(88200 i \, a b^{2} + 88200 \, b^{3}\right)} c^{4} + {\left({\left(1411200 i \, a^{2} b + 1411200 \, a b^{2}\right)} c^{2} + {\left(-1411200 i \, a b^{2} - 1411200 \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left({\left(-846720 i \, a^{2} b - 846720 \, a b^{2}\right)} c^{3} + {\left(1270080 i \, a b^{2} + 1270080 \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left({\left(264600 i \, a^{2} b + 264600 \, a b^{2}\right)} c^{4} + {\left(-529200 i \, a b^{2} - 529200 \, b^{3}\right)} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - 2520 \, {\left(168 \, {\left(a^{2} b - i \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} - 14 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{5} + 240 \, {\left(a b^{2} - i \, b^{3} - 2 \, {\left(a^{2} b - i \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + 35 \, {\left(a b^{2} - i \, b^{3}\right)} c^{4} + 560 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} c^{2} - {\left(a b^{2} - i \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} - 168 \, {\left(2 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{3} - 3 \, {\left(a b^{2} - i \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + 105 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} c^{4} - 2 \, {\left(a b^{2} - i \, b^{3}\right)} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} {\rm Li}_{4}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}}{-i \, a + b}) + {\left(141120 \, {\left(a^{2} b + i \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} + 8820 \, {\left(a^{2} b + i \, a b^{2}\right)} c^{6} + 241920 \, {\left(a b^{2} + i \, b^{3} - 2 \, {\left(a^{2} b + i \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} - 26460 \, {\left(a b^{2} + i \, b^{3}\right)} c^{5} + 705600 \, {\left({\left(a^{2} b + i \, a b^{2}\right)} c^{2} - {\left(a b^{2} + i \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} - 282240 \, {\left(2 \, {\left(a^{2} b + i \, a b^{2}\right)} c^{3} - 3 \, {\left(a b^{2} + i \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + 264600 \, {\left({\left(a^{2} b + i \, a b^{2}\right)} c^{4} - 2 \, {\left(a b^{2} + i \, b^{3}\right)} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} - 35280 \, {\left(2 \, {\left(a^{2} b + i \, a b^{2}\right)} c^{5} - 5 \, {\left(a b^{2} + i \, b^{3}\right)} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)} + 1260 \, {\left(112 \, {\left(a^{2} b - i \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} + 7 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{6} + 192 \, {\left(a b^{2} - i \, b^{3} - 2 \, {\left(a^{2} b - i \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} - 21 \, {\left(a b^{2} - i \, b^{3}\right)} c^{5} + 560 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} c^{2} - {\left(a b^{2} - i \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} - 224 \, {\left(2 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{3} - 3 \, {\left(a b^{2} - i \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + 210 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} c^{4} - 2 \, {\left(a b^{2} - i \, b^{3}\right)} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} - 28 \, {\left(2 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{5} - 5 \, {\left(a b^{2} - i \, b^{3}\right)} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left({\left(141120 i \, a^{2} b + 141120 \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} + {\left(8820 i \, a^{2} b + 8820 \, a b^{2}\right)} c^{6} + {\left(241920 i \, a b^{2} + 241920 \, b^{3} + {\left(-483840 i \, a^{2} b - 483840 \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + {\left(-26460 i \, a b^{2} - 26460 \, b^{3}\right)} c^{5} + {\left({\left(705600 i \, a^{2} b + 705600 \, a b^{2}\right)} c^{2} + {\left(-705600 i \, a b^{2} - 705600 \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + {\left({\left(-564480 i \, a^{2} b - 564480 \, a b^{2}\right)} c^{3} + {\left(846720 i \, a b^{2} + 846720 \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left({\left(264600 i \, a^{2} b + 264600 \, a b^{2}\right)} c^{4} + {\left(-529200 i \, a b^{2} - 529200 \, b^{3}\right)} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left({\left(-70560 i \, a^{2} b - 70560 \, a b^{2}\right)} c^{5} + {\left(176400 i \, a b^{2} + 176400 \, b^{3}\right)} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} {\rm Li}_{3}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}}{-i \, a + b}) + {\left({\left(35 i \, a^{3} + 105 \, a^{2} b - 105 i \, a b^{2} - 35 \, b^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{9} + {\left(630 \, a b^{2} - 630 i \, b^{3} + {\left(-315 i \, a^{3} - 945 \, a^{2} b + 945 i \, a b^{2} + 315 \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{8} - 5040 \, {\left(a b^{2} - i \, b^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)} c^{7} + {\left({\left(1260 i \, a^{3} + 3780 \, a^{2} b - 3780 i \, a b^{2} - 1260 \, b^{3}\right)} c^{2} - 5040 \, {\left(a b^{2} - i \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{7} + {\left({\left(-2940 i \, a^{3} - 8820 \, a^{2} b + 8820 i \, a b^{2} + 2940 \, b^{3}\right)} c^{3} + 17640 \, {\left(a b^{2} - i \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} + {\left({\left(4410 i \, a^{3} + 13230 \, a^{2} b - 13230 i \, a b^{2} - 4410 \, b^{3}\right)} c^{4} - 35280 \, {\left(a b^{2} - i \, b^{3}\right)} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + {\left({\left(-4410 i \, a^{3} - 13230 \, a^{2} b + 13230 i \, a b^{2} + 4410 \, b^{3}\right)} c^{5} + 44100 \, {\left(a b^{2} - i \, b^{3}\right)} c^{4}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + {\left({\left(2940 i \, a^{3} + 8820 \, a^{2} b - 8820 i \, a b^{2} - 2940 \, b^{3}\right)} c^{6} - 35280 \, {\left(a b^{2} - i \, b^{3}\right)} c^{5}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left({\left(-1260 i \, a^{3} - 3780 \, a^{2} b + 3780 i \, a b^{2} + 1260 \, b^{3}\right)} c^{7} + 17640 \, {\left(a b^{2} - i \, b^{3}\right)} c^{6}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)}{315 \, a^{5} + 315 i \, a^{4} b + 630 \, a^{3} b^{2} + 630 i \, a^{2} b^{3} + 315 \, a b^{4} + 315 i \, b^{5} + {\left(315 \, a^{5} - 315 i \, a^{4} b + 630 \, a^{3} b^{2} - 630 i \, a^{2} b^{3} + 315 \, a b^{4} - 315 i \, b^{5}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left(315 i \, a^{5} + 315 \, a^{4} b + 630 i \, a^{3} b^{2} + 630 \, a^{2} b^{3} + 315 i \, a b^{4} + 315 \, b^{5}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)}\right)}}{d^{9}}"," ",0,"3*((2*a*b*log(b*tan(d*x^(1/3) + c) + a)/(a^4 + 2*a^2*b^2 + b^4) - a*b*log(tan(d*x^(1/3) + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + (a^2 - b^2)*(d*x^(1/3) + c)/(a^4 + 2*a^2*b^2 + b^4) - b/(a^3 + a*b^2 + (a^2*b + b^3)*tan(d*x^(1/3) + c)))*c^8 + ((35*a^3 - 35*I*a^2*b + 35*a*b^2 - 35*I*b^3)*(d*x^(1/3) + c)^9 - (315*a^3 - 315*I*a^2*b + 315*a*b^2 - 315*I*b^3)*(d*x^(1/3) + c)^8*c + (1260*a^3 - 1260*I*a^2*b + 1260*a*b^2 - 1260*I*b^3)*(d*x^(1/3) + c)^7*c^2 - (2940*a^3 - 2940*I*a^2*b + 2940*a*b^2 - 2940*I*b^3)*(d*x^(1/3) + c)^6*c^3 + (4410*a^3 - 4410*I*a^2*b + 4410*a*b^2 - 4410*I*b^3)*(d*x^(1/3) + c)^5*c^4 - (4410*a^3 - 4410*I*a^2*b + 4410*a*b^2 - 4410*I*b^3)*(d*x^(1/3) + c)^4*c^5 + (2940*a^3 - 2940*I*a^2*b + 2940*a*b^2 - 2940*I*b^3)*(d*x^(1/3) + c)^3*c^6 - (1260*a^3 - 1260*I*a^2*b + 1260*a*b^2 - 1260*I*b^3)*(d*x^(1/3) + c)^2*c^7 + ((-2520*I*a*b^2 - 2520*b^3)*c^7*cos(2*d*x^(1/3) + 2*c) + 2520*(a*b^2 - I*b^3)*c^7*sin(2*d*x^(1/3) + 2*c) + (-2520*I*a*b^2 + 2520*b^3)*c^7)*arctan2(-b*cos(2*d*x^(1/3) + 2*c) + a*sin(2*d*x^(1/3) + 2*c) + b, a*cos(2*d*x^(1/3) + 2*c) + b*sin(2*d*x^(1/3) + 2*c) + a) + ((-10080*I*a^2*b + 10080*a*b^2)*(d*x^(1/3) + c)^8 + (-23040*I*a*b^2 + 23040*b^3 + (46080*I*a^2*b - 46080*a*b^2)*c)*(d*x^(1/3) + c)^7 + ((-94080*I*a^2*b + 94080*a*b^2)*c^2 + (94080*I*a*b^2 - 94080*b^3)*c)*(d*x^(1/3) + c)^6 + ((112896*I*a^2*b - 112896*a*b^2)*c^3 + (-169344*I*a*b^2 + 169344*b^3)*c^2)*(d*x^(1/3) + c)^5 + ((-88200*I*a^2*b + 88200*a*b^2)*c^4 + (176400*I*a*b^2 - 176400*b^3)*c^3)*(d*x^(1/3) + c)^4 + ((47040*I*a^2*b - 47040*a*b^2)*c^5 + (-117600*I*a*b^2 + 117600*b^3)*c^4)*(d*x^(1/3) + c)^3 + ((-17640*I*a^2*b + 17640*a*b^2)*c^6 + (52920*I*a*b^2 - 52920*b^3)*c^5)*(d*x^(1/3) + c)^2 + ((5040*I*a^2*b - 5040*a*b^2)*c^7 + (-17640*I*a*b^2 + 17640*b^3)*c^6)*(d*x^(1/3) + c) + ((-10080*I*a^2*b - 10080*a*b^2)*(d*x^(1/3) + c)^8 + (-23040*I*a*b^2 - 23040*b^3 + (46080*I*a^2*b + 46080*a*b^2)*c)*(d*x^(1/3) + c)^7 + ((-94080*I*a^2*b - 94080*a*b^2)*c^2 + (94080*I*a*b^2 + 94080*b^3)*c)*(d*x^(1/3) + c)^6 + ((112896*I*a^2*b + 112896*a*b^2)*c^3 + (-169344*I*a*b^2 - 169344*b^3)*c^2)*(d*x^(1/3) + c)^5 + ((-88200*I*a^2*b - 88200*a*b^2)*c^4 + (176400*I*a*b^2 + 176400*b^3)*c^3)*(d*x^(1/3) + c)^4 + ((47040*I*a^2*b + 47040*a*b^2)*c^5 + (-117600*I*a*b^2 - 117600*b^3)*c^4)*(d*x^(1/3) + c)^3 + ((-17640*I*a^2*b - 17640*a*b^2)*c^6 + (52920*I*a*b^2 + 52920*b^3)*c^5)*(d*x^(1/3) + c)^2 + ((5040*I*a^2*b + 5040*a*b^2)*c^7 + (-17640*I*a*b^2 - 17640*b^3)*c^6)*(d*x^(1/3) + c))*cos(2*d*x^(1/3) + 2*c) + 24*(420*(a^2*b - I*a*b^2)*(d*x^(1/3) + c)^8 + 960*(a*b^2 - I*b^3 - 2*(a^2*b - I*a*b^2)*c)*(d*x^(1/3) + c)^7 + 3920*((a^2*b - I*a*b^2)*c^2 - (a*b^2 - I*b^3)*c)*(d*x^(1/3) + c)^6 - 2352*(2*(a^2*b - I*a*b^2)*c^3 - 3*(a*b^2 - I*b^3)*c^2)*(d*x^(1/3) + c)^5 + 3675*((a^2*b - I*a*b^2)*c^4 - 2*(a*b^2 - I*b^3)*c^3)*(d*x^(1/3) + c)^4 - 980*(2*(a^2*b - I*a*b^2)*c^5 - 5*(a*b^2 - I*b^3)*c^4)*(d*x^(1/3) + c)^3 + 735*((a^2*b - I*a*b^2)*c^6 - 3*(a*b^2 - I*b^3)*c^5)*(d*x^(1/3) + c)^2 - 105*(2*(a^2*b - I*a*b^2)*c^7 - 7*(a*b^2 - I*b^3)*c^6)*(d*x^(1/3) + c))*sin(2*d*x^(1/3) + 2*c))*arctan2((2*a*b*cos(2*d*x^(1/3) + 2*c) - (a^2 - b^2)*sin(2*d*x^(1/3) + 2*c))/(a^2 + b^2), (2*a*b*sin(2*d*x^(1/3) + 2*c) + a^2 + b^2 + (a^2 - b^2)*cos(2*d*x^(1/3) + 2*c))/(a^2 + b^2)) + ((35*a^3 - 105*I*a^2*b - 105*a*b^2 + 35*I*b^3)*(d*x^(1/3) + c)^9 + (-630*I*a*b^2 - 630*b^3 - (315*a^3 - 945*I*a^2*b - 945*a*b^2 + 315*I*b^3)*c)*(d*x^(1/3) + c)^8 + (5040*I*a*b^2 + 5040*b^3)*(d*x^(1/3) + c)*c^7 + ((1260*a^3 - 3780*I*a^2*b - 3780*a*b^2 + 1260*I*b^3)*c^2 + (5040*I*a*b^2 + 5040*b^3)*c)*(d*x^(1/3) + c)^7 - ((2940*a^3 - 8820*I*a^2*b - 8820*a*b^2 + 2940*I*b^3)*c^3 - (-17640*I*a*b^2 - 17640*b^3)*c^2)*(d*x^(1/3) + c)^6 + ((4410*a^3 - 13230*I*a^2*b - 13230*a*b^2 + 4410*I*b^3)*c^4 + (35280*I*a*b^2 + 35280*b^3)*c^3)*(d*x^(1/3) + c)^5 - ((4410*a^3 - 13230*I*a^2*b - 13230*a*b^2 + 4410*I*b^3)*c^5 - (-44100*I*a*b^2 - 44100*b^3)*c^4)*(d*x^(1/3) + c)^4 + ((2940*a^3 - 8820*I*a^2*b - 8820*a*b^2 + 2940*I*b^3)*c^6 + (35280*I*a*b^2 + 35280*b^3)*c^5)*(d*x^(1/3) + c)^3 - ((1260*a^3 - 3780*I*a^2*b - 3780*a*b^2 + 1260*I*b^3)*c^7 - (-17640*I*a*b^2 - 17640*b^3)*c^6)*(d*x^(1/3) + c)^2)*cos(2*d*x^(1/3) + 2*c) + ((-40320*I*a^2*b + 40320*a*b^2)*(d*x^(1/3) + c)^7 + (2520*I*a^2*b - 2520*a*b^2)*c^7 + (-80640*I*a*b^2 + 80640*b^3 + (161280*I*a^2*b - 161280*a*b^2)*c)*(d*x^(1/3) + c)^6 + (-8820*I*a*b^2 + 8820*b^3)*c^6 + ((-282240*I*a^2*b + 282240*a*b^2)*c^2 + (282240*I*a*b^2 - 282240*b^3)*c)*(d*x^(1/3) + c)^5 + ((282240*I*a^2*b - 282240*a*b^2)*c^3 + (-423360*I*a*b^2 + 423360*b^3)*c^2)*(d*x^(1/3) + c)^4 + ((-176400*I*a^2*b + 176400*a*b^2)*c^4 + (352800*I*a*b^2 - 352800*b^3)*c^3)*(d*x^(1/3) + c)^3 + ((70560*I*a^2*b - 70560*a*b^2)*c^5 + (-176400*I*a*b^2 + 176400*b^3)*c^4)*(d*x^(1/3) + c)^2 + ((-17640*I*a^2*b + 17640*a*b^2)*c^6 + (52920*I*a*b^2 - 52920*b^3)*c^5)*(d*x^(1/3) + c) + ((-40320*I*a^2*b - 40320*a*b^2)*(d*x^(1/3) + c)^7 + (2520*I*a^2*b + 2520*a*b^2)*c^7 + (-80640*I*a*b^2 - 80640*b^3 + (161280*I*a^2*b + 161280*a*b^2)*c)*(d*x^(1/3) + c)^6 + (-8820*I*a*b^2 - 8820*b^3)*c^6 + ((-282240*I*a^2*b - 282240*a*b^2)*c^2 + (282240*I*a*b^2 + 282240*b^3)*c)*(d*x^(1/3) + c)^5 + ((282240*I*a^2*b + 282240*a*b^2)*c^3 + (-423360*I*a*b^2 - 423360*b^3)*c^2)*(d*x^(1/3) + c)^4 + ((-176400*I*a^2*b - 176400*a*b^2)*c^4 + (352800*I*a*b^2 + 352800*b^3)*c^3)*(d*x^(1/3) + c)^3 + ((70560*I*a^2*b + 70560*a*b^2)*c^5 + (-176400*I*a*b^2 - 176400*b^3)*c^4)*(d*x^(1/3) + c)^2 + ((-17640*I*a^2*b - 17640*a*b^2)*c^6 + (52920*I*a*b^2 + 52920*b^3)*c^5)*(d*x^(1/3) + c))*cos(2*d*x^(1/3) + 2*c) + 1260*(32*(a^2*b - I*a*b^2)*(d*x^(1/3) + c)^7 - 2*(a^2*b - I*a*b^2)*c^7 + 64*(a*b^2 - I*b^3 - 2*(a^2*b - I*a*b^2)*c)*(d*x^(1/3) + c)^6 + 7*(a*b^2 - I*b^3)*c^6 + 224*((a^2*b - I*a*b^2)*c^2 - (a*b^2 - I*b^3)*c)*(d*x^(1/3) + c)^5 - 112*(2*(a^2*b - I*a*b^2)*c^3 - 3*(a*b^2 - I*b^3)*c^2)*(d*x^(1/3) + c)^4 + 140*((a^2*b - I*a*b^2)*c^4 - 2*(a*b^2 - I*b^3)*c^3)*(d*x^(1/3) + c)^3 - 28*(2*(a^2*b - I*a*b^2)*c^5 - 5*(a*b^2 - I*b^3)*c^4)*(d*x^(1/3) + c)^2 + 14*((a^2*b - I*a*b^2)*c^6 - 3*(a*b^2 - I*b^3)*c^5)*(d*x^(1/3) + c))*sin(2*d*x^(1/3) + 2*c))*dilog((I*a + b)*e^(2*I*d*x^(1/3) + 2*I*c)/(-I*a + b)) - (1260*(a*b^2 - I*b^3)*c^7*cos(2*d*x^(1/3) + 2*c) - (-1260*I*a*b^2 - 1260*b^3)*c^7*sin(2*d*x^(1/3) + 2*c) + 1260*(a*b^2 + I*b^3)*c^7)*log((a^2 + b^2)*cos(2*d*x^(1/3) + 2*c)^2 + 4*a*b*sin(2*d*x^(1/3) + 2*c) + (a^2 + b^2)*sin(2*d*x^(1/3) + 2*c)^2 + a^2 + b^2 + 2*(a^2 - b^2)*cos(2*d*x^(1/3) + 2*c)) + (5040*(a^2*b + I*a*b^2)*(d*x^(1/3) + c)^8 + 11520*(a*b^2 + I*b^3 - 2*(a^2*b + I*a*b^2)*c)*(d*x^(1/3) + c)^7 + 47040*((a^2*b + I*a*b^2)*c^2 - (a*b^2 + I*b^3)*c)*(d*x^(1/3) + c)^6 - 28224*(2*(a^2*b + I*a*b^2)*c^3 - 3*(a*b^2 + I*b^3)*c^2)*(d*x^(1/3) + c)^5 + 44100*((a^2*b + I*a*b^2)*c^4 - 2*(a*b^2 + I*b^3)*c^3)*(d*x^(1/3) + c)^4 - 11760*(2*(a^2*b + I*a*b^2)*c^5 - 5*(a*b^2 + I*b^3)*c^4)*(d*x^(1/3) + c)^3 + 8820*((a^2*b + I*a*b^2)*c^6 - 3*(a*b^2 + I*b^3)*c^5)*(d*x^(1/3) + c)^2 - 1260*(2*(a^2*b + I*a*b^2)*c^7 - 7*(a*b^2 + I*b^3)*c^6)*(d*x^(1/3) + c) + 12*(420*(a^2*b - I*a*b^2)*(d*x^(1/3) + c)^8 + 960*(a*b^2 - I*b^3 - 2*(a^2*b - I*a*b^2)*c)*(d*x^(1/3) + c)^7 + 3920*((a^2*b - I*a*b^2)*c^2 - (a*b^2 - I*b^3)*c)*(d*x^(1/3) + c)^6 - 2352*(2*(a^2*b - I*a*b^2)*c^3 - 3*(a*b^2 - I*b^3)*c^2)*(d*x^(1/3) + c)^5 + 3675*((a^2*b - I*a*b^2)*c^4 - 2*(a*b^2 - I*b^3)*c^3)*(d*x^(1/3) + c)^4 - 980*(2*(a^2*b - I*a*b^2)*c^5 - 5*(a*b^2 - I*b^3)*c^4)*(d*x^(1/3) + c)^3 + 735*((a^2*b - I*a*b^2)*c^6 - 3*(a*b^2 - I*b^3)*c^5)*(d*x^(1/3) + c)^2 - 105*(2*(a^2*b - I*a*b^2)*c^7 - 7*(a*b^2 - I*b^3)*c^6)*(d*x^(1/3) + c))*cos(2*d*x^(1/3) + 2*c) + ((5040*I*a^2*b + 5040*a*b^2)*(d*x^(1/3) + c)^8 + (11520*I*a*b^2 + 11520*b^3 + (-23040*I*a^2*b - 23040*a*b^2)*c)*(d*x^(1/3) + c)^7 + ((47040*I*a^2*b + 47040*a*b^2)*c^2 + (-47040*I*a*b^2 - 47040*b^3)*c)*(d*x^(1/3) + c)^6 + ((-56448*I*a^2*b - 56448*a*b^2)*c^3 + (84672*I*a*b^2 + 84672*b^3)*c^2)*(d*x^(1/3) + c)^5 + ((44100*I*a^2*b + 44100*a*b^2)*c^4 + (-88200*I*a*b^2 - 88200*b^3)*c^3)*(d*x^(1/3) + c)^4 + ((-23520*I*a^2*b - 23520*a*b^2)*c^5 + (58800*I*a*b^2 + 58800*b^3)*c^4)*(d*x^(1/3) + c)^3 + ((8820*I*a^2*b + 8820*a*b^2)*c^6 + (-26460*I*a*b^2 - 26460*b^3)*c^5)*(d*x^(1/3) + c)^2 + ((-2520*I*a^2*b - 2520*a*b^2)*c^7 + (8820*I*a*b^2 + 8820*b^3)*c^6)*(d*x^(1/3) + c))*sin(2*d*x^(1/3) + 2*c))*log(((a^2 + b^2)*cos(2*d*x^(1/3) + 2*c)^2 + 4*a*b*sin(2*d*x^(1/3) + 2*c) + (a^2 + b^2)*sin(2*d*x^(1/3) + 2*c)^2 + a^2 + b^2 + 2*(a^2 - b^2)*cos(2*d*x^(1/3) + 2*c))/(a^2 + b^2)) - (1587600*a^2*b + 1587600*I*a*b^2 + 1587600*(a^2*b - I*a*b^2)*cos(2*d*x^(1/3) + 2*c) - (-1587600*I*a^2*b - 1587600*a*b^2)*sin(2*d*x^(1/3) + 2*c))*polylog(9, (I*a + b)*e^(2*I*d*x^(1/3) + 2*I*c)/(-I*a + b)) + (907200*I*a*b^2 - 907200*b^3 + (3175200*I*a^2*b - 3175200*a*b^2)*(d*x^(1/3) + c) + (-1814400*I*a^2*b + 1814400*a*b^2)*c + (907200*I*a*b^2 + 907200*b^3 + (3175200*I*a^2*b + 3175200*a*b^2)*(d*x^(1/3) + c) + (-1814400*I*a^2*b - 1814400*a*b^2)*c)*cos(2*d*x^(1/3) + 2*c) - 453600*(2*a*b^2 - 2*I*b^3 + 7*(a^2*b - I*a*b^2)*(d*x^(1/3) + c) - 4*(a^2*b - I*a*b^2)*c)*sin(2*d*x^(1/3) + 2*c))*polylog(8, (I*a + b)*e^(2*I*d*x^(1/3) + 2*I*c)/(-I*a + b)) + (3175200*(a^2*b + I*a*b^2)*(d*x^(1/3) + c)^2 + 1058400*(a^2*b + I*a*b^2)*c^2 + 1814400*(a*b^2 + I*b^3 - 2*(a^2*b + I*a*b^2)*c)*(d*x^(1/3) + c) - 1058400*(a*b^2 + I*b^3)*c + 151200*(21*(a^2*b - I*a*b^2)*(d*x^(1/3) + c)^2 + 7*(a^2*b - I*a*b^2)*c^2 + 12*(a*b^2 - I*b^3 - 2*(a^2*b - I*a*b^2)*c)*(d*x^(1/3) + c) - 7*(a*b^2 - I*b^3)*c)*cos(2*d*x^(1/3) + 2*c) + ((3175200*I*a^2*b + 3175200*a*b^2)*(d*x^(1/3) + c)^2 + (1058400*I*a^2*b + 1058400*a*b^2)*c^2 + (1814400*I*a*b^2 + 1814400*b^3 + (-3628800*I*a^2*b - 3628800*a*b^2)*c)*(d*x^(1/3) + c) + (-1058400*I*a*b^2 - 1058400*b^3)*c)*sin(2*d*x^(1/3) + 2*c))*polylog(7, (I*a + b)*e^(2*I*d*x^(1/3) + 2*I*c)/(-I*a + b)) + ((-2116800*I*a^2*b + 2116800*a*b^2)*(d*x^(1/3) + c)^3 + (423360*I*a^2*b - 423360*a*b^2)*c^3 + (-1814400*I*a*b^2 + 1814400*b^3 + (3628800*I*a^2*b - 3628800*a*b^2)*c)*(d*x^(1/3) + c)^2 + (-635040*I*a*b^2 + 635040*b^3)*c^2 + ((-2116800*I*a^2*b + 2116800*a*b^2)*c^2 + (2116800*I*a*b^2 - 2116800*b^3)*c)*(d*x^(1/3) + c) + ((-2116800*I*a^2*b - 2116800*a*b^2)*(d*x^(1/3) + c)^3 + (423360*I*a^2*b + 423360*a*b^2)*c^3 + (-1814400*I*a*b^2 - 1814400*b^3 + (3628800*I*a^2*b + 3628800*a*b^2)*c)*(d*x^(1/3) + c)^2 + (-635040*I*a*b^2 - 635040*b^3)*c^2 + ((-2116800*I*a^2*b - 2116800*a*b^2)*c^2 + (2116800*I*a*b^2 + 2116800*b^3)*c)*(d*x^(1/3) + c))*cos(2*d*x^(1/3) + 2*c) + 30240*(70*(a^2*b - I*a*b^2)*(d*x^(1/3) + c)^3 - 14*(a^2*b - I*a*b^2)*c^3 + 60*(a*b^2 - I*b^3 - 2*(a^2*b - I*a*b^2)*c)*(d*x^(1/3) + c)^2 + 21*(a*b^2 - I*b^3)*c^2 + 70*((a^2*b - I*a*b^2)*c^2 - (a*b^2 - I*b^3)*c)*(d*x^(1/3) + c))*sin(2*d*x^(1/3) + 2*c))*polylog(6, (I*a + b)*e^(2*I*d*x^(1/3) + 2*I*c)/(-I*a + b)) - (1058400*(a^2*b + I*a*b^2)*(d*x^(1/3) + c)^4 + 132300*(a^2*b + I*a*b^2)*c^4 + 1209600*(a*b^2 + I*b^3 - 2*(a^2*b + I*a*b^2)*c)*(d*x^(1/3) + c)^3 - 264600*(a*b^2 + I*b^3)*c^3 + 2116800*((a^2*b + I*a*b^2)*c^2 - (a*b^2 + I*b^3)*c)*(d*x^(1/3) + c)^2 - 423360*(2*(a^2*b + I*a*b^2)*c^3 - 3*(a*b^2 + I*b^3)*c^2)*(d*x^(1/3) + c) + 3780*(280*(a^2*b - I*a*b^2)*(d*x^(1/3) + c)^4 + 35*(a^2*b - I*a*b^2)*c^4 + 320*(a*b^2 - I*b^3 - 2*(a^2*b - I*a*b^2)*c)*(d*x^(1/3) + c)^3 - 70*(a*b^2 - I*b^3)*c^3 + 560*((a^2*b - I*a*b^2)*c^2 - (a*b^2 - I*b^3)*c)*(d*x^(1/3) + c)^2 - 112*(2*(a^2*b - I*a*b^2)*c^3 - 3*(a*b^2 - I*b^3)*c^2)*(d*x^(1/3) + c))*cos(2*d*x^(1/3) + 2*c) - ((-1058400*I*a^2*b - 1058400*a*b^2)*(d*x^(1/3) + c)^4 + (-132300*I*a^2*b - 132300*a*b^2)*c^4 + (-1209600*I*a*b^2 - 1209600*b^3 + (2419200*I*a^2*b + 2419200*a*b^2)*c)*(d*x^(1/3) + c)^3 + (264600*I*a*b^2 + 264600*b^3)*c^3 + ((-2116800*I*a^2*b - 2116800*a*b^2)*c^2 + (2116800*I*a*b^2 + 2116800*b^3)*c)*(d*x^(1/3) + c)^2 + ((846720*I*a^2*b + 846720*a*b^2)*c^3 + (-1270080*I*a*b^2 - 1270080*b^3)*c^2)*(d*x^(1/3) + c))*sin(2*d*x^(1/3) + 2*c))*polylog(5, (I*a + b)*e^(2*I*d*x^(1/3) + 2*I*c)/(-I*a + b)) + ((423360*I*a^2*b - 423360*a*b^2)*(d*x^(1/3) + c)^5 + (-35280*I*a^2*b + 35280*a*b^2)*c^5 + (604800*I*a*b^2 - 604800*b^3 + (-1209600*I*a^2*b + 1209600*a*b^2)*c)*(d*x^(1/3) + c)^4 + (88200*I*a*b^2 - 88200*b^3)*c^4 + ((1411200*I*a^2*b - 1411200*a*b^2)*c^2 + (-1411200*I*a*b^2 + 1411200*b^3)*c)*(d*x^(1/3) + c)^3 + ((-846720*I*a^2*b + 846720*a*b^2)*c^3 + (1270080*I*a*b^2 - 1270080*b^3)*c^2)*(d*x^(1/3) + c)^2 + ((264600*I*a^2*b - 264600*a*b^2)*c^4 + (-529200*I*a*b^2 + 529200*b^3)*c^3)*(d*x^(1/3) + c) + ((423360*I*a^2*b + 423360*a*b^2)*(d*x^(1/3) + c)^5 + (-35280*I*a^2*b - 35280*a*b^2)*c^5 + (604800*I*a*b^2 + 604800*b^3 + (-1209600*I*a^2*b - 1209600*a*b^2)*c)*(d*x^(1/3) + c)^4 + (88200*I*a*b^2 + 88200*b^3)*c^4 + ((1411200*I*a^2*b + 1411200*a*b^2)*c^2 + (-1411200*I*a*b^2 - 1411200*b^3)*c)*(d*x^(1/3) + c)^3 + ((-846720*I*a^2*b - 846720*a*b^2)*c^3 + (1270080*I*a*b^2 + 1270080*b^3)*c^2)*(d*x^(1/3) + c)^2 + ((264600*I*a^2*b + 264600*a*b^2)*c^4 + (-529200*I*a*b^2 - 529200*b^3)*c^3)*(d*x^(1/3) + c))*cos(2*d*x^(1/3) + 2*c) - 2520*(168*(a^2*b - I*a*b^2)*(d*x^(1/3) + c)^5 - 14*(a^2*b - I*a*b^2)*c^5 + 240*(a*b^2 - I*b^3 - 2*(a^2*b - I*a*b^2)*c)*(d*x^(1/3) + c)^4 + 35*(a*b^2 - I*b^3)*c^4 + 560*((a^2*b - I*a*b^2)*c^2 - (a*b^2 - I*b^3)*c)*(d*x^(1/3) + c)^3 - 168*(2*(a^2*b - I*a*b^2)*c^3 - 3*(a*b^2 - I*b^3)*c^2)*(d*x^(1/3) + c)^2 + 105*((a^2*b - I*a*b^2)*c^4 - 2*(a*b^2 - I*b^3)*c^3)*(d*x^(1/3) + c))*sin(2*d*x^(1/3) + 2*c))*polylog(4, (I*a + b)*e^(2*I*d*x^(1/3) + 2*I*c)/(-I*a + b)) + (141120*(a^2*b + I*a*b^2)*(d*x^(1/3) + c)^6 + 8820*(a^2*b + I*a*b^2)*c^6 + 241920*(a*b^2 + I*b^3 - 2*(a^2*b + I*a*b^2)*c)*(d*x^(1/3) + c)^5 - 26460*(a*b^2 + I*b^3)*c^5 + 705600*((a^2*b + I*a*b^2)*c^2 - (a*b^2 + I*b^3)*c)*(d*x^(1/3) + c)^4 - 282240*(2*(a^2*b + I*a*b^2)*c^3 - 3*(a*b^2 + I*b^3)*c^2)*(d*x^(1/3) + c)^3 + 264600*((a^2*b + I*a*b^2)*c^4 - 2*(a*b^2 + I*b^3)*c^3)*(d*x^(1/3) + c)^2 - 35280*(2*(a^2*b + I*a*b^2)*c^5 - 5*(a*b^2 + I*b^3)*c^4)*(d*x^(1/3) + c) + 1260*(112*(a^2*b - I*a*b^2)*(d*x^(1/3) + c)^6 + 7*(a^2*b - I*a*b^2)*c^6 + 192*(a*b^2 - I*b^3 - 2*(a^2*b - I*a*b^2)*c)*(d*x^(1/3) + c)^5 - 21*(a*b^2 - I*b^3)*c^5 + 560*((a^2*b - I*a*b^2)*c^2 - (a*b^2 - I*b^3)*c)*(d*x^(1/3) + c)^4 - 224*(2*(a^2*b - I*a*b^2)*c^3 - 3*(a*b^2 - I*b^3)*c^2)*(d*x^(1/3) + c)^3 + 210*((a^2*b - I*a*b^2)*c^4 - 2*(a*b^2 - I*b^3)*c^3)*(d*x^(1/3) + c)^2 - 28*(2*(a^2*b - I*a*b^2)*c^5 - 5*(a*b^2 - I*b^3)*c^4)*(d*x^(1/3) + c))*cos(2*d*x^(1/3) + 2*c) + ((141120*I*a^2*b + 141120*a*b^2)*(d*x^(1/3) + c)^6 + (8820*I*a^2*b + 8820*a*b^2)*c^6 + (241920*I*a*b^2 + 241920*b^3 + (-483840*I*a^2*b - 483840*a*b^2)*c)*(d*x^(1/3) + c)^5 + (-26460*I*a*b^2 - 26460*b^3)*c^5 + ((705600*I*a^2*b + 705600*a*b^2)*c^2 + (-705600*I*a*b^2 - 705600*b^3)*c)*(d*x^(1/3) + c)^4 + ((-564480*I*a^2*b - 564480*a*b^2)*c^3 + (846720*I*a*b^2 + 846720*b^3)*c^2)*(d*x^(1/3) + c)^3 + ((264600*I*a^2*b + 264600*a*b^2)*c^4 + (-529200*I*a*b^2 - 529200*b^3)*c^3)*(d*x^(1/3) + c)^2 + ((-70560*I*a^2*b - 70560*a*b^2)*c^5 + (176400*I*a*b^2 + 176400*b^3)*c^4)*(d*x^(1/3) + c))*sin(2*d*x^(1/3) + 2*c))*polylog(3, (I*a + b)*e^(2*I*d*x^(1/3) + 2*I*c)/(-I*a + b)) + ((35*I*a^3 + 105*a^2*b - 105*I*a*b^2 - 35*b^3)*(d*x^(1/3) + c)^9 + (630*a*b^2 - 630*I*b^3 + (-315*I*a^3 - 945*a^2*b + 945*I*a*b^2 + 315*b^3)*c)*(d*x^(1/3) + c)^8 - 5040*(a*b^2 - I*b^3)*(d*x^(1/3) + c)*c^7 + ((1260*I*a^3 + 3780*a^2*b - 3780*I*a*b^2 - 1260*b^3)*c^2 - 5040*(a*b^2 - I*b^3)*c)*(d*x^(1/3) + c)^7 + ((-2940*I*a^3 - 8820*a^2*b + 8820*I*a*b^2 + 2940*b^3)*c^3 + 17640*(a*b^2 - I*b^3)*c^2)*(d*x^(1/3) + c)^6 + ((4410*I*a^3 + 13230*a^2*b - 13230*I*a*b^2 - 4410*b^3)*c^4 - 35280*(a*b^2 - I*b^3)*c^3)*(d*x^(1/3) + c)^5 + ((-4410*I*a^3 - 13230*a^2*b + 13230*I*a*b^2 + 4410*b^3)*c^5 + 44100*(a*b^2 - I*b^3)*c^4)*(d*x^(1/3) + c)^4 + ((2940*I*a^3 + 8820*a^2*b - 8820*I*a*b^2 - 2940*b^3)*c^6 - 35280*(a*b^2 - I*b^3)*c^5)*(d*x^(1/3) + c)^3 + ((-1260*I*a^3 - 3780*a^2*b + 3780*I*a*b^2 + 1260*b^3)*c^7 + 17640*(a*b^2 - I*b^3)*c^6)*(d*x^(1/3) + c)^2)*sin(2*d*x^(1/3) + 2*c))/(315*a^5 + 315*I*a^4*b + 630*a^3*b^2 + 630*I*a^2*b^3 + 315*a*b^4 + 315*I*b^5 + (315*a^5 - 315*I*a^4*b + 630*a^3*b^2 - 630*I*a^2*b^3 + 315*a*b^4 - 315*I*b^5)*cos(2*d*x^(1/3) + 2*c) + (315*I*a^5 + 315*a^4*b + 630*I*a^3*b^2 + 630*a^2*b^3 + 315*I*a*b^4 + 315*b^5)*sin(2*d*x^(1/3) + 2*c)))/d^9","B",0
63,1,4350,0,3.382802," ","integrate(x/(a+b*tan(c+d*x^(1/3)))^2,x, algorithm=""maxima"")","-\frac{3 \, {\left({\left(\frac{2 \, a b \log\left(b \tan\left(d x^{\frac{1}{3}} + c\right) + a\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{a b \log\left(\tan\left(d x^{\frac{1}{3}} + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(a^{2} - b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{b}{a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} \tan\left(d x^{\frac{1}{3}} + c\right)}\right)} c^{5} - \frac{{\left(5 \, a^{3} - 5 i \, a^{2} b + 5 \, a b^{2} - 5 i \, b^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} - {\left(30 \, a^{3} - 30 i \, a^{2} b + 30 \, a b^{2} - 30 i \, b^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} c + {\left(75 \, a^{3} - 75 i \, a^{2} b + 75 \, a b^{2} - 75 i \, b^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} c^{2} - {\left(100 \, a^{3} - 100 i \, a^{2} b + 100 \, a b^{2} - 100 i \, b^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} c^{3} + {\left(75 \, a^{3} - 75 i \, a^{2} b + 75 \, a b^{2} - 75 i \, b^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} c^{4} + {\left({\left(150 i \, a b^{2} + 150 \, b^{3}\right)} c^{4} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - 150 \, {\left(a b^{2} - i \, b^{3}\right)} c^{4} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left(150 i \, a b^{2} - 150 \, b^{3}\right)} c^{4}\right)} \arctan\left(-b \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + a \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + b, a \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + b \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + a\right) + {\left({\left(-192 i \, a^{2} b + 192 \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + {\left(-300 i \, a b^{2} + 300 \, b^{3} + {\left(600 i \, a^{2} b - 600 \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + {\left({\left(-800 i \, a^{2} b + 800 \, a b^{2}\right)} c^{2} + {\left(800 i \, a b^{2} - 800 \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left({\left(600 i \, a^{2} b - 600 \, a b^{2}\right)} c^{3} + {\left(-900 i \, a b^{2} + 900 \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left({\left(-300 i \, a^{2} b + 300 \, a b^{2}\right)} c^{4} + {\left(600 i \, a b^{2} - 600 \, b^{3}\right)} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)} + {\left({\left(-192 i \, a^{2} b - 192 \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + {\left(-300 i \, a b^{2} - 300 \, b^{3} + {\left(600 i \, a^{2} b + 600 \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + {\left({\left(-800 i \, a^{2} b - 800 \, a b^{2}\right)} c^{2} + {\left(800 i \, a b^{2} + 800 \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left({\left(600 i \, a^{2} b + 600 \, a b^{2}\right)} c^{3} + {\left(-900 i \, a b^{2} - 900 \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left({\left(-300 i \, a^{2} b - 300 \, a b^{2}\right)} c^{4} + {\left(600 i \, a b^{2} + 600 \, b^{3}\right)} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 4 \, {\left(48 \, {\left(a^{2} b - i \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + 75 \, {\left(a b^{2} - i \, b^{3} - 2 \, {\left(a^{2} b - i \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + 200 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} c^{2} - {\left(a b^{2} - i \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} - 75 \, {\left(2 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{3} - 3 \, {\left(a b^{2} - i \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + 75 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} c^{4} - 2 \, {\left(a b^{2} - i \, b^{3}\right)} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} \arctan\left(\frac{2 \, a b \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - {\left(a^{2} - b^{2}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)}{a^{2} + b^{2}}, \frac{2 \, a b \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + a^{2} + b^{2} + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)}{a^{2} + b^{2}}\right) + {\left({\left(5 \, a^{3} - 15 i \, a^{2} b - 15 \, a b^{2} + 5 i \, b^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} + {\left(-60 i \, a b^{2} - 60 \, b^{3} - {\left(30 \, a^{3} - 90 i \, a^{2} b - 90 \, a b^{2} + 30 i \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + {\left(-300 i \, a b^{2} - 300 \, b^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)} c^{4} + {\left({\left(75 \, a^{3} - 225 i \, a^{2} b - 225 \, a b^{2} + 75 i \, b^{3}\right)} c^{2} + {\left(300 i \, a b^{2} + 300 \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} - {\left({\left(100 \, a^{3} - 300 i \, a^{2} b - 300 \, a b^{2} + 100 i \, b^{3}\right)} c^{3} - {\left(-600 i \, a b^{2} - 600 \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left({\left(75 \, a^{3} - 225 i \, a^{2} b - 225 \, a b^{2} + 75 i \, b^{3}\right)} c^{4} + {\left(600 i \, a b^{2} + 600 \, b^{3}\right)} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left({\left(-480 i \, a^{2} b + 480 \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + {\left(-150 i \, a^{2} b + 150 \, a b^{2}\right)} c^{4} + {\left(-600 i \, a b^{2} + 600 \, b^{3} + {\left(1200 i \, a^{2} b - 1200 \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left(300 i \, a b^{2} - 300 \, b^{3}\right)} c^{3} + {\left({\left(-1200 i \, a^{2} b + 1200 \, a b^{2}\right)} c^{2} + {\left(1200 i \, a b^{2} - 1200 \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left({\left(600 i \, a^{2} b - 600 \, a b^{2}\right)} c^{3} + {\left(-900 i \, a b^{2} + 900 \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)} + {\left({\left(-480 i \, a^{2} b - 480 \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + {\left(-150 i \, a^{2} b - 150 \, a b^{2}\right)} c^{4} + {\left(-600 i \, a b^{2} - 600 \, b^{3} + {\left(1200 i \, a^{2} b + 1200 \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left(300 i \, a b^{2} + 300 \, b^{3}\right)} c^{3} + {\left({\left(-1200 i \, a^{2} b - 1200 \, a b^{2}\right)} c^{2} + {\left(1200 i \, a b^{2} + 1200 \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left({\left(600 i \, a^{2} b + 600 \, a b^{2}\right)} c^{3} + {\left(-900 i \, a b^{2} - 900 \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 30 \, {\left(16 \, {\left(a^{2} b - i \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + 5 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{4} + 20 \, {\left(a b^{2} - i \, b^{3} - 2 \, {\left(a^{2} b - i \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} - 10 \, {\left(a b^{2} - i \, b^{3}\right)} c^{3} + 40 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} c^{2} - {\left(a b^{2} - i \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} - 10 \, {\left(2 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{3} - 3 \, {\left(a b^{2} - i \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} {\rm Li}_2\left(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}}{-i \, a + b}\right) + {\left(75 \, {\left(a b^{2} - i \, b^{3}\right)} c^{4} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left(75 i \, a b^{2} + 75 \, b^{3}\right)} c^{4} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 75 \, {\left(a b^{2} + i \, b^{3}\right)} c^{4}\right)} \log\left({\left(a^{2} + b^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + 4 \, a b \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right) + {\left(96 \, {\left(a^{2} b + i \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + 150 \, {\left(a b^{2} + i \, b^{3} - 2 \, {\left(a^{2} b + i \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + 400 \, {\left({\left(a^{2} b + i \, a b^{2}\right)} c^{2} - {\left(a b^{2} + i \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} - 150 \, {\left(2 \, {\left(a^{2} b + i \, a b^{2}\right)} c^{3} - 3 \, {\left(a b^{2} + i \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + 150 \, {\left({\left(a^{2} b + i \, a b^{2}\right)} c^{4} - 2 \, {\left(a b^{2} + i \, b^{3}\right)} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)} + 2 \, {\left(48 \, {\left(a^{2} b - i \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + 75 \, {\left(a b^{2} - i \, b^{3} - 2 \, {\left(a^{2} b - i \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + 200 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} c^{2} - {\left(a b^{2} - i \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} - 75 \, {\left(2 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{3} - 3 \, {\left(a b^{2} - i \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + 75 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} c^{4} - 2 \, {\left(a b^{2} - i \, b^{3}\right)} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left({\left(96 i \, a^{2} b + 96 \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + {\left(150 i \, a b^{2} + 150 \, b^{3} + {\left(-300 i \, a^{2} b - 300 \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + {\left({\left(400 i \, a^{2} b + 400 \, a b^{2}\right)} c^{2} + {\left(-400 i \, a b^{2} - 400 \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left({\left(-300 i \, a^{2} b - 300 \, a b^{2}\right)} c^{3} + {\left(450 i \, a b^{2} + 450 \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left({\left(150 i \, a^{2} b + 150 \, a b^{2}\right)} c^{4} + {\left(-300 i \, a b^{2} - 300 \, b^{3}\right)} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} \log\left(\frac{{\left(a^{2} + b^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + 4 \, a b \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)}{a^{2} + b^{2}}\right) + {\left(-720 i \, a^{2} b + 720 \, a b^{2} + {\left(-720 i \, a^{2} b - 720 \, a b^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 720 \, {\left(a^{2} b - i \, a b^{2}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} {\rm Li}_{6}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}}{-i \, a + b}) - {\left(450 \, a b^{2} + 450 i \, b^{3} + 1440 \, {\left(a^{2} b + i \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)} - 900 \, {\left(a^{2} b + i \, a b^{2}\right)} c + 90 \, {\left(5 \, a b^{2} - 5 i \, b^{3} + 16 \, {\left(a^{2} b - i \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)} - 10 \, {\left(a^{2} b - i \, a b^{2}\right)} c\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - {\left(-450 i \, a b^{2} - 450 \, b^{3} + {\left(-1440 i \, a^{2} b - 1440 \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)} + {\left(900 i \, a^{2} b + 900 \, a b^{2}\right)} c\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} {\rm Li}_{5}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}}{-i \, a + b}) + {\left({\left(1440 i \, a^{2} b - 1440 \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left(600 i \, a^{2} b - 600 \, a b^{2}\right)} c^{2} + {\left(900 i \, a b^{2} - 900 \, b^{3} + {\left(-1800 i \, a^{2} b + 1800 \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)} + {\left(-600 i \, a b^{2} + 600 \, b^{3}\right)} c + {\left({\left(1440 i \, a^{2} b + 1440 \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left(600 i \, a^{2} b + 600 \, a b^{2}\right)} c^{2} + {\left(900 i \, a b^{2} + 900 \, b^{3} + {\left(-1800 i \, a^{2} b - 1800 \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)} + {\left(-600 i \, a b^{2} - 600 \, b^{3}\right)} c\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - 60 \, {\left(24 \, {\left(a^{2} b - i \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + 10 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{2} + 15 \, {\left(a b^{2} - i \, b^{3} - 2 \, {\left(a^{2} b - i \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)} - 10 \, {\left(a b^{2} - i \, b^{3}\right)} c\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} {\rm Li}_{4}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}}{-i \, a + b}) + {\left(960 \, {\left(a^{2} b + i \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} - 300 \, {\left(a^{2} b + i \, a b^{2}\right)} c^{3} + 900 \, {\left(a b^{2} + i \, b^{3} - 2 \, {\left(a^{2} b + i \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + 450 \, {\left(a b^{2} + i \, b^{3}\right)} c^{2} + 1200 \, {\left({\left(a^{2} b + i \, a b^{2}\right)} c^{2} - {\left(a b^{2} + i \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)} + 30 \, {\left(32 \, {\left(a^{2} b - i \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} - 10 \, {\left(a^{2} b - i \, a b^{2}\right)} c^{3} + 30 \, {\left(a b^{2} - i \, b^{3} - 2 \, {\left(a^{2} b - i \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + 15 \, {\left(a b^{2} - i \, b^{3}\right)} c^{2} + 40 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} c^{2} - {\left(a b^{2} - i \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left({\left(960 i \, a^{2} b + 960 \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left(-300 i \, a^{2} b - 300 \, a b^{2}\right)} c^{3} + {\left(900 i \, a b^{2} + 900 \, b^{3} + {\left(-1800 i \, a^{2} b - 1800 \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left(450 i \, a b^{2} + 450 \, b^{3}\right)} c^{2} + {\left({\left(1200 i \, a^{2} b + 1200 \, a b^{2}\right)} c^{2} + {\left(-1200 i \, a b^{2} - 1200 \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} {\rm Li}_{3}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}}{-i \, a + b}) + {\left({\left(5 i \, a^{3} + 15 \, a^{2} b - 15 i \, a b^{2} - 5 \, b^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{6} + {\left(60 \, a b^{2} - 60 i \, b^{3} + {\left(-30 i \, a^{3} - 90 \, a^{2} b + 90 i \, a b^{2} + 30 \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{5} + 300 \, {\left(a b^{2} - i \, b^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)} c^{4} + {\left({\left(75 i \, a^{3} + 225 \, a^{2} b - 225 i \, a b^{2} - 75 \, b^{3}\right)} c^{2} - 300 \, {\left(a b^{2} - i \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{4} + {\left({\left(-100 i \, a^{3} - 300 \, a^{2} b + 300 i \, a b^{2} + 100 \, b^{3}\right)} c^{3} + 600 \, {\left(a b^{2} - i \, b^{3}\right)} c^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left({\left(75 i \, a^{3} + 225 \, a^{2} b - 225 i \, a b^{2} - 75 \, b^{3}\right)} c^{4} - 600 \, {\left(a b^{2} - i \, b^{3}\right)} c^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)}{30 \, a^{5} + 30 i \, a^{4} b + 60 \, a^{3} b^{2} + 60 i \, a^{2} b^{3} + 30 \, a b^{4} + 30 i \, b^{5} + {\left(30 \, a^{5} - 30 i \, a^{4} b + 60 \, a^{3} b^{2} - 60 i \, a^{2} b^{3} + 30 \, a b^{4} - 30 i \, b^{5}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left(30 i \, a^{5} + 30 \, a^{4} b + 60 i \, a^{3} b^{2} + 60 \, a^{2} b^{3} + 30 i \, a b^{4} + 30 \, b^{5}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)}\right)}}{d^{6}}"," ",0,"-3*((2*a*b*log(b*tan(d*x^(1/3) + c) + a)/(a^4 + 2*a^2*b^2 + b^4) - a*b*log(tan(d*x^(1/3) + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + (a^2 - b^2)*(d*x^(1/3) + c)/(a^4 + 2*a^2*b^2 + b^4) - b/(a^3 + a*b^2 + (a^2*b + b^3)*tan(d*x^(1/3) + c)))*c^5 - ((5*a^3 - 5*I*a^2*b + 5*a*b^2 - 5*I*b^3)*(d*x^(1/3) + c)^6 - (30*a^3 - 30*I*a^2*b + 30*a*b^2 - 30*I*b^3)*(d*x^(1/3) + c)^5*c + (75*a^3 - 75*I*a^2*b + 75*a*b^2 - 75*I*b^3)*(d*x^(1/3) + c)^4*c^2 - (100*a^3 - 100*I*a^2*b + 100*a*b^2 - 100*I*b^3)*(d*x^(1/3) + c)^3*c^3 + (75*a^3 - 75*I*a^2*b + 75*a*b^2 - 75*I*b^3)*(d*x^(1/3) + c)^2*c^4 + ((150*I*a*b^2 + 150*b^3)*c^4*cos(2*d*x^(1/3) + 2*c) - 150*(a*b^2 - I*b^3)*c^4*sin(2*d*x^(1/3) + 2*c) + (150*I*a*b^2 - 150*b^3)*c^4)*arctan2(-b*cos(2*d*x^(1/3) + 2*c) + a*sin(2*d*x^(1/3) + 2*c) + b, a*cos(2*d*x^(1/3) + 2*c) + b*sin(2*d*x^(1/3) + 2*c) + a) + ((-192*I*a^2*b + 192*a*b^2)*(d*x^(1/3) + c)^5 + (-300*I*a*b^2 + 300*b^3 + (600*I*a^2*b - 600*a*b^2)*c)*(d*x^(1/3) + c)^4 + ((-800*I*a^2*b + 800*a*b^2)*c^2 + (800*I*a*b^2 - 800*b^3)*c)*(d*x^(1/3) + c)^3 + ((600*I*a^2*b - 600*a*b^2)*c^3 + (-900*I*a*b^2 + 900*b^3)*c^2)*(d*x^(1/3) + c)^2 + ((-300*I*a^2*b + 300*a*b^2)*c^4 + (600*I*a*b^2 - 600*b^3)*c^3)*(d*x^(1/3) + c) + ((-192*I*a^2*b - 192*a*b^2)*(d*x^(1/3) + c)^5 + (-300*I*a*b^2 - 300*b^3 + (600*I*a^2*b + 600*a*b^2)*c)*(d*x^(1/3) + c)^4 + ((-800*I*a^2*b - 800*a*b^2)*c^2 + (800*I*a*b^2 + 800*b^3)*c)*(d*x^(1/3) + c)^3 + ((600*I*a^2*b + 600*a*b^2)*c^3 + (-900*I*a*b^2 - 900*b^3)*c^2)*(d*x^(1/3) + c)^2 + ((-300*I*a^2*b - 300*a*b^2)*c^4 + (600*I*a*b^2 + 600*b^3)*c^3)*(d*x^(1/3) + c))*cos(2*d*x^(1/3) + 2*c) + 4*(48*(a^2*b - I*a*b^2)*(d*x^(1/3) + c)^5 + 75*(a*b^2 - I*b^3 - 2*(a^2*b - I*a*b^2)*c)*(d*x^(1/3) + c)^4 + 200*((a^2*b - I*a*b^2)*c^2 - (a*b^2 - I*b^3)*c)*(d*x^(1/3) + c)^3 - 75*(2*(a^2*b - I*a*b^2)*c^3 - 3*(a*b^2 - I*b^3)*c^2)*(d*x^(1/3) + c)^2 + 75*((a^2*b - I*a*b^2)*c^4 - 2*(a*b^2 - I*b^3)*c^3)*(d*x^(1/3) + c))*sin(2*d*x^(1/3) + 2*c))*arctan2((2*a*b*cos(2*d*x^(1/3) + 2*c) - (a^2 - b^2)*sin(2*d*x^(1/3) + 2*c))/(a^2 + b^2), (2*a*b*sin(2*d*x^(1/3) + 2*c) + a^2 + b^2 + (a^2 - b^2)*cos(2*d*x^(1/3) + 2*c))/(a^2 + b^2)) + ((5*a^3 - 15*I*a^2*b - 15*a*b^2 + 5*I*b^3)*(d*x^(1/3) + c)^6 + (-60*I*a*b^2 - 60*b^3 - (30*a^3 - 90*I*a^2*b - 90*a*b^2 + 30*I*b^3)*c)*(d*x^(1/3) + c)^5 + (-300*I*a*b^2 - 300*b^3)*(d*x^(1/3) + c)*c^4 + ((75*a^3 - 225*I*a^2*b - 225*a*b^2 + 75*I*b^3)*c^2 + (300*I*a*b^2 + 300*b^3)*c)*(d*x^(1/3) + c)^4 - ((100*a^3 - 300*I*a^2*b - 300*a*b^2 + 100*I*b^3)*c^3 - (-600*I*a*b^2 - 600*b^3)*c^2)*(d*x^(1/3) + c)^3 + ((75*a^3 - 225*I*a^2*b - 225*a*b^2 + 75*I*b^3)*c^4 + (600*I*a*b^2 + 600*b^3)*c^3)*(d*x^(1/3) + c)^2)*cos(2*d*x^(1/3) + 2*c) + ((-480*I*a^2*b + 480*a*b^2)*(d*x^(1/3) + c)^4 + (-150*I*a^2*b + 150*a*b^2)*c^4 + (-600*I*a*b^2 + 600*b^3 + (1200*I*a^2*b - 1200*a*b^2)*c)*(d*x^(1/3) + c)^3 + (300*I*a*b^2 - 300*b^3)*c^3 + ((-1200*I*a^2*b + 1200*a*b^2)*c^2 + (1200*I*a*b^2 - 1200*b^3)*c)*(d*x^(1/3) + c)^2 + ((600*I*a^2*b - 600*a*b^2)*c^3 + (-900*I*a*b^2 + 900*b^3)*c^2)*(d*x^(1/3) + c) + ((-480*I*a^2*b - 480*a*b^2)*(d*x^(1/3) + c)^4 + (-150*I*a^2*b - 150*a*b^2)*c^4 + (-600*I*a*b^2 - 600*b^3 + (1200*I*a^2*b + 1200*a*b^2)*c)*(d*x^(1/3) + c)^3 + (300*I*a*b^2 + 300*b^3)*c^3 + ((-1200*I*a^2*b - 1200*a*b^2)*c^2 + (1200*I*a*b^2 + 1200*b^3)*c)*(d*x^(1/3) + c)^2 + ((600*I*a^2*b + 600*a*b^2)*c^3 + (-900*I*a*b^2 - 900*b^3)*c^2)*(d*x^(1/3) + c))*cos(2*d*x^(1/3) + 2*c) + 30*(16*(a^2*b - I*a*b^2)*(d*x^(1/3) + c)^4 + 5*(a^2*b - I*a*b^2)*c^4 + 20*(a*b^2 - I*b^3 - 2*(a^2*b - I*a*b^2)*c)*(d*x^(1/3) + c)^3 - 10*(a*b^2 - I*b^3)*c^3 + 40*((a^2*b - I*a*b^2)*c^2 - (a*b^2 - I*b^3)*c)*(d*x^(1/3) + c)^2 - 10*(2*(a^2*b - I*a*b^2)*c^3 - 3*(a*b^2 - I*b^3)*c^2)*(d*x^(1/3) + c))*sin(2*d*x^(1/3) + 2*c))*dilog((I*a + b)*e^(2*I*d*x^(1/3) + 2*I*c)/(-I*a + b)) + (75*(a*b^2 - I*b^3)*c^4*cos(2*d*x^(1/3) + 2*c) + (75*I*a*b^2 + 75*b^3)*c^4*sin(2*d*x^(1/3) + 2*c) + 75*(a*b^2 + I*b^3)*c^4)*log((a^2 + b^2)*cos(2*d*x^(1/3) + 2*c)^2 + 4*a*b*sin(2*d*x^(1/3) + 2*c) + (a^2 + b^2)*sin(2*d*x^(1/3) + 2*c)^2 + a^2 + b^2 + 2*(a^2 - b^2)*cos(2*d*x^(1/3) + 2*c)) + (96*(a^2*b + I*a*b^2)*(d*x^(1/3) + c)^5 + 150*(a*b^2 + I*b^3 - 2*(a^2*b + I*a*b^2)*c)*(d*x^(1/3) + c)^4 + 400*((a^2*b + I*a*b^2)*c^2 - (a*b^2 + I*b^3)*c)*(d*x^(1/3) + c)^3 - 150*(2*(a^2*b + I*a*b^2)*c^3 - 3*(a*b^2 + I*b^3)*c^2)*(d*x^(1/3) + c)^2 + 150*((a^2*b + I*a*b^2)*c^4 - 2*(a*b^2 + I*b^3)*c^3)*(d*x^(1/3) + c) + 2*(48*(a^2*b - I*a*b^2)*(d*x^(1/3) + c)^5 + 75*(a*b^2 - I*b^3 - 2*(a^2*b - I*a*b^2)*c)*(d*x^(1/3) + c)^4 + 200*((a^2*b - I*a*b^2)*c^2 - (a*b^2 - I*b^3)*c)*(d*x^(1/3) + c)^3 - 75*(2*(a^2*b - I*a*b^2)*c^3 - 3*(a*b^2 - I*b^3)*c^2)*(d*x^(1/3) + c)^2 + 75*((a^2*b - I*a*b^2)*c^4 - 2*(a*b^2 - I*b^3)*c^3)*(d*x^(1/3) + c))*cos(2*d*x^(1/3) + 2*c) + ((96*I*a^2*b + 96*a*b^2)*(d*x^(1/3) + c)^5 + (150*I*a*b^2 + 150*b^3 + (-300*I*a^2*b - 300*a*b^2)*c)*(d*x^(1/3) + c)^4 + ((400*I*a^2*b + 400*a*b^2)*c^2 + (-400*I*a*b^2 - 400*b^3)*c)*(d*x^(1/3) + c)^3 + ((-300*I*a^2*b - 300*a*b^2)*c^3 + (450*I*a*b^2 + 450*b^3)*c^2)*(d*x^(1/3) + c)^2 + ((150*I*a^2*b + 150*a*b^2)*c^4 + (-300*I*a*b^2 - 300*b^3)*c^3)*(d*x^(1/3) + c))*sin(2*d*x^(1/3) + 2*c))*log(((a^2 + b^2)*cos(2*d*x^(1/3) + 2*c)^2 + 4*a*b*sin(2*d*x^(1/3) + 2*c) + (a^2 + b^2)*sin(2*d*x^(1/3) + 2*c)^2 + a^2 + b^2 + 2*(a^2 - b^2)*cos(2*d*x^(1/3) + 2*c))/(a^2 + b^2)) + (-720*I*a^2*b + 720*a*b^2 + (-720*I*a^2*b - 720*a*b^2)*cos(2*d*x^(1/3) + 2*c) + 720*(a^2*b - I*a*b^2)*sin(2*d*x^(1/3) + 2*c))*polylog(6, (I*a + b)*e^(2*I*d*x^(1/3) + 2*I*c)/(-I*a + b)) - (450*a*b^2 + 450*I*b^3 + 1440*(a^2*b + I*a*b^2)*(d*x^(1/3) + c) - 900*(a^2*b + I*a*b^2)*c + 90*(5*a*b^2 - 5*I*b^3 + 16*(a^2*b - I*a*b^2)*(d*x^(1/3) + c) - 10*(a^2*b - I*a*b^2)*c)*cos(2*d*x^(1/3) + 2*c) - (-450*I*a*b^2 - 450*b^3 + (-1440*I*a^2*b - 1440*a*b^2)*(d*x^(1/3) + c) + (900*I*a^2*b + 900*a*b^2)*c)*sin(2*d*x^(1/3) + 2*c))*polylog(5, (I*a + b)*e^(2*I*d*x^(1/3) + 2*I*c)/(-I*a + b)) + ((1440*I*a^2*b - 1440*a*b^2)*(d*x^(1/3) + c)^2 + (600*I*a^2*b - 600*a*b^2)*c^2 + (900*I*a*b^2 - 900*b^3 + (-1800*I*a^2*b + 1800*a*b^2)*c)*(d*x^(1/3) + c) + (-600*I*a*b^2 + 600*b^3)*c + ((1440*I*a^2*b + 1440*a*b^2)*(d*x^(1/3) + c)^2 + (600*I*a^2*b + 600*a*b^2)*c^2 + (900*I*a*b^2 + 900*b^3 + (-1800*I*a^2*b - 1800*a*b^2)*c)*(d*x^(1/3) + c) + (-600*I*a*b^2 - 600*b^3)*c)*cos(2*d*x^(1/3) + 2*c) - 60*(24*(a^2*b - I*a*b^2)*(d*x^(1/3) + c)^2 + 10*(a^2*b - I*a*b^2)*c^2 + 15*(a*b^2 - I*b^3 - 2*(a^2*b - I*a*b^2)*c)*(d*x^(1/3) + c) - 10*(a*b^2 - I*b^3)*c)*sin(2*d*x^(1/3) + 2*c))*polylog(4, (I*a + b)*e^(2*I*d*x^(1/3) + 2*I*c)/(-I*a + b)) + (960*(a^2*b + I*a*b^2)*(d*x^(1/3) + c)^3 - 300*(a^2*b + I*a*b^2)*c^3 + 900*(a*b^2 + I*b^3 - 2*(a^2*b + I*a*b^2)*c)*(d*x^(1/3) + c)^2 + 450*(a*b^2 + I*b^3)*c^2 + 1200*((a^2*b + I*a*b^2)*c^2 - (a*b^2 + I*b^3)*c)*(d*x^(1/3) + c) + 30*(32*(a^2*b - I*a*b^2)*(d*x^(1/3) + c)^3 - 10*(a^2*b - I*a*b^2)*c^3 + 30*(a*b^2 - I*b^3 - 2*(a^2*b - I*a*b^2)*c)*(d*x^(1/3) + c)^2 + 15*(a*b^2 - I*b^3)*c^2 + 40*((a^2*b - I*a*b^2)*c^2 - (a*b^2 - I*b^3)*c)*(d*x^(1/3) + c))*cos(2*d*x^(1/3) + 2*c) + ((960*I*a^2*b + 960*a*b^2)*(d*x^(1/3) + c)^3 + (-300*I*a^2*b - 300*a*b^2)*c^3 + (900*I*a*b^2 + 900*b^3 + (-1800*I*a^2*b - 1800*a*b^2)*c)*(d*x^(1/3) + c)^2 + (450*I*a*b^2 + 450*b^3)*c^2 + ((1200*I*a^2*b + 1200*a*b^2)*c^2 + (-1200*I*a*b^2 - 1200*b^3)*c)*(d*x^(1/3) + c))*sin(2*d*x^(1/3) + 2*c))*polylog(3, (I*a + b)*e^(2*I*d*x^(1/3) + 2*I*c)/(-I*a + b)) + ((5*I*a^3 + 15*a^2*b - 15*I*a*b^2 - 5*b^3)*(d*x^(1/3) + c)^6 + (60*a*b^2 - 60*I*b^3 + (-30*I*a^3 - 90*a^2*b + 90*I*a*b^2 + 30*b^3)*c)*(d*x^(1/3) + c)^5 + 300*(a*b^2 - I*b^3)*(d*x^(1/3) + c)*c^4 + ((75*I*a^3 + 225*a^2*b - 225*I*a*b^2 - 75*b^3)*c^2 - 300*(a*b^2 - I*b^3)*c)*(d*x^(1/3) + c)^4 + ((-100*I*a^3 - 300*a^2*b + 300*I*a*b^2 + 100*b^3)*c^3 + 600*(a*b^2 - I*b^3)*c^2)*(d*x^(1/3) + c)^3 + ((75*I*a^3 + 225*a^2*b - 225*I*a*b^2 - 75*b^3)*c^4 - 600*(a*b^2 - I*b^3)*c^3)*(d*x^(1/3) + c)^2)*sin(2*d*x^(1/3) + 2*c))/(30*a^5 + 30*I*a^4*b + 60*a^3*b^2 + 60*I*a^2*b^3 + 30*a*b^4 + 30*I*b^5 + (30*a^5 - 30*I*a^4*b + 60*a^3*b^2 - 60*I*a^2*b^3 + 30*a*b^4 - 30*I*b^5)*cos(2*d*x^(1/3) + 2*c) + (30*I*a^5 + 30*a^4*b + 60*I*a^3*b^2 + 60*a^2*b^3 + 30*I*a*b^4 + 30*b^5)*sin(2*d*x^(1/3) + 2*c)))/d^6","B",0
64,1,1746,0,2.166477," ","integrate(1/(a+b*tan(c+d*x^(1/3)))^2,x, algorithm=""maxima"")","\frac{3 \, {\left({\left(\frac{2 \, a b \log\left(b \tan\left(d x^{\frac{1}{3}} + c\right) + a\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{a b \log\left(\tan\left(d x^{\frac{1}{3}} + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(a^{2} - b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{b}{a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} \tan\left(d x^{\frac{1}{3}} + c\right)}\right)} c^{2} + \frac{{\left(a^{3} - i \, a^{2} b + a b^{2} - i \, b^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} - {\left(3 \, a^{3} - 3 i \, a^{2} b + 3 \, a b^{2} - 3 i \, b^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} c + {\left({\left(-6 i \, a b^{2} - 6 \, b^{3}\right)} c \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 6 \, {\left(a b^{2} - i \, b^{3}\right)} c \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left(-6 i \, a b^{2} + 6 \, b^{3}\right)} c\right)} \arctan\left(-b \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + a \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + b, a \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + b \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + a\right) + {\left({\left(-6 i \, a^{2} b + 6 \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left(-6 i \, a b^{2} + 6 \, b^{3} + {\left(12 i \, a^{2} b - 12 \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)} + {\left({\left(-6 i \, a^{2} b - 6 \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left(-6 i \, a b^{2} - 6 \, b^{3} + {\left(12 i \, a^{2} b + 12 \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 6 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left(a b^{2} - i \, b^{3} - 2 \, {\left(a^{2} b - i \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} \arctan\left(\frac{2 \, a b \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - {\left(a^{2} - b^{2}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)}{a^{2} + b^{2}}, \frac{2 \, a b \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + a^{2} + b^{2} + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)}{a^{2} + b^{2}}\right) + {\left({\left(a^{3} - 3 i \, a^{2} b - 3 \, a b^{2} + i \, b^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left(-6 i \, a b^{2} - 6 \, b^{3} - {\left(3 \, a^{3} - 9 i \, a^{2} b - 9 \, a b^{2} + 3 i \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left(12 i \, a b^{2} + 12 \, b^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)} c\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left(-3 i \, a b^{2} + 3 \, b^{3} + {\left(-6 i \, a^{2} b + 6 \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)} + {\left(6 i \, a^{2} b - 6 \, a b^{2}\right)} c + {\left(-3 i \, a b^{2} - 3 \, b^{3} + {\left(-6 i \, a^{2} b - 6 \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)} + {\left(6 i \, a^{2} b + 6 \, a b^{2}\right)} c\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 3 \, {\left(a b^{2} - i \, b^{3} + 2 \, {\left(a^{2} b - i \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)} - 2 \, {\left(a^{2} b - i \, a b^{2}\right)} c\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} {\rm Li}_2\left(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}}{-i \, a + b}\right) - {\left(3 \, {\left(a b^{2} - i \, b^{3}\right)} c \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - {\left(-3 i \, a b^{2} - 3 \, b^{3}\right)} c \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + 3 \, {\left(a b^{2} + i \, b^{3}\right)} c\right)} \log\left({\left(a^{2} + b^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + 4 \, a b \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right) + {\left(3 \, {\left(a^{2} b + i \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + 3 \, {\left(a b^{2} + i \, b^{3} - 2 \, {\left(a^{2} b + i \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)} + 3 \, {\left({\left(a^{2} b - i \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left(a b^{2} - i \, b^{3} - 2 \, {\left(a^{2} b - i \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left({\left(3 i \, a^{2} b + 3 \, a b^{2}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} + {\left(3 i \, a b^{2} + 3 \, b^{3} + {\left(-6 i \, a^{2} b - 6 \, a b^{2}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} \log\left(\frac{{\left(a^{2} + b^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + 4 \, a b \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)}{a^{2} + b^{2}}\right) + {\left(3 \, a^{2} b + 3 i \, a b^{2} + 3 \, {\left(a^{2} b - i \, a b^{2}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left(3 i \, a^{2} b + 3 \, a b^{2}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} {\rm Li}_{3}(\frac{{\left(i \, a + b\right)} e^{\left(2 i \, d x^{\frac{1}{3}} + 2 i \, c\right)}}{-i \, a + b}) + {\left({\left(i \, a^{3} + 3 \, a^{2} b - 3 i \, a b^{2} - b^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{3} + {\left(6 \, a b^{2} - 6 i \, b^{3} + {\left(-3 i \, a^{3} - 9 \, a^{2} b + 9 i \, a b^{2} + 3 \, b^{3}\right)} c\right)} {\left(d x^{\frac{1}{3}} + c\right)}^{2} - 12 \, {\left(a b^{2} - i \, b^{3}\right)} {\left(d x^{\frac{1}{3}} + c\right)} c\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)}{3 \, a^{5} + 3 i \, a^{4} b + 6 \, a^{3} b^{2} + 6 i \, a^{2} b^{3} + 3 \, a b^{4} + 3 i \, b^{5} + {\left(3 \, a^{5} - 3 i \, a^{4} b + 6 \, a^{3} b^{2} - 6 i \, a^{2} b^{3} + 3 \, a b^{4} - 3 i \, b^{5}\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left(3 i \, a^{5} + 3 \, a^{4} b + 6 i \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 3 i \, a b^{4} + 3 \, b^{5}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)}\right)}}{d^{3}}"," ",0,"3*((2*a*b*log(b*tan(d*x^(1/3) + c) + a)/(a^4 + 2*a^2*b^2 + b^4) - a*b*log(tan(d*x^(1/3) + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + (a^2 - b^2)*(d*x^(1/3) + c)/(a^4 + 2*a^2*b^2 + b^4) - b/(a^3 + a*b^2 + (a^2*b + b^3)*tan(d*x^(1/3) + c)))*c^2 + ((a^3 - I*a^2*b + a*b^2 - I*b^3)*(d*x^(1/3) + c)^3 - (3*a^3 - 3*I*a^2*b + 3*a*b^2 - 3*I*b^3)*(d*x^(1/3) + c)^2*c + ((-6*I*a*b^2 - 6*b^3)*c*cos(2*d*x^(1/3) + 2*c) + 6*(a*b^2 - I*b^3)*c*sin(2*d*x^(1/3) + 2*c) + (-6*I*a*b^2 + 6*b^3)*c)*arctan2(-b*cos(2*d*x^(1/3) + 2*c) + a*sin(2*d*x^(1/3) + 2*c) + b, a*cos(2*d*x^(1/3) + 2*c) + b*sin(2*d*x^(1/3) + 2*c) + a) + ((-6*I*a^2*b + 6*a*b^2)*(d*x^(1/3) + c)^2 + (-6*I*a*b^2 + 6*b^3 + (12*I*a^2*b - 12*a*b^2)*c)*(d*x^(1/3) + c) + ((-6*I*a^2*b - 6*a*b^2)*(d*x^(1/3) + c)^2 + (-6*I*a*b^2 - 6*b^3 + (12*I*a^2*b + 12*a*b^2)*c)*(d*x^(1/3) + c))*cos(2*d*x^(1/3) + 2*c) + 6*((a^2*b - I*a*b^2)*(d*x^(1/3) + c)^2 + (a*b^2 - I*b^3 - 2*(a^2*b - I*a*b^2)*c)*(d*x^(1/3) + c))*sin(2*d*x^(1/3) + 2*c))*arctan2((2*a*b*cos(2*d*x^(1/3) + 2*c) - (a^2 - b^2)*sin(2*d*x^(1/3) + 2*c))/(a^2 + b^2), (2*a*b*sin(2*d*x^(1/3) + 2*c) + a^2 + b^2 + (a^2 - b^2)*cos(2*d*x^(1/3) + 2*c))/(a^2 + b^2)) + ((a^3 - 3*I*a^2*b - 3*a*b^2 + I*b^3)*(d*x^(1/3) + c)^3 + (-6*I*a*b^2 - 6*b^3 - (3*a^3 - 9*I*a^2*b - 9*a*b^2 + 3*I*b^3)*c)*(d*x^(1/3) + c)^2 + (12*I*a*b^2 + 12*b^3)*(d*x^(1/3) + c)*c)*cos(2*d*x^(1/3) + 2*c) + (-3*I*a*b^2 + 3*b^3 + (-6*I*a^2*b + 6*a*b^2)*(d*x^(1/3) + c) + (6*I*a^2*b - 6*a*b^2)*c + (-3*I*a*b^2 - 3*b^3 + (-6*I*a^2*b - 6*a*b^2)*(d*x^(1/3) + c) + (6*I*a^2*b + 6*a*b^2)*c)*cos(2*d*x^(1/3) + 2*c) + 3*(a*b^2 - I*b^3 + 2*(a^2*b - I*a*b^2)*(d*x^(1/3) + c) - 2*(a^2*b - I*a*b^2)*c)*sin(2*d*x^(1/3) + 2*c))*dilog((I*a + b)*e^(2*I*d*x^(1/3) + 2*I*c)/(-I*a + b)) - (3*(a*b^2 - I*b^3)*c*cos(2*d*x^(1/3) + 2*c) - (-3*I*a*b^2 - 3*b^3)*c*sin(2*d*x^(1/3) + 2*c) + 3*(a*b^2 + I*b^3)*c)*log((a^2 + b^2)*cos(2*d*x^(1/3) + 2*c)^2 + 4*a*b*sin(2*d*x^(1/3) + 2*c) + (a^2 + b^2)*sin(2*d*x^(1/3) + 2*c)^2 + a^2 + b^2 + 2*(a^2 - b^2)*cos(2*d*x^(1/3) + 2*c)) + (3*(a^2*b + I*a*b^2)*(d*x^(1/3) + c)^2 + 3*(a*b^2 + I*b^3 - 2*(a^2*b + I*a*b^2)*c)*(d*x^(1/3) + c) + 3*((a^2*b - I*a*b^2)*(d*x^(1/3) + c)^2 + (a*b^2 - I*b^3 - 2*(a^2*b - I*a*b^2)*c)*(d*x^(1/3) + c))*cos(2*d*x^(1/3) + 2*c) + ((3*I*a^2*b + 3*a*b^2)*(d*x^(1/3) + c)^2 + (3*I*a*b^2 + 3*b^3 + (-6*I*a^2*b - 6*a*b^2)*c)*(d*x^(1/3) + c))*sin(2*d*x^(1/3) + 2*c))*log(((a^2 + b^2)*cos(2*d*x^(1/3) + 2*c)^2 + 4*a*b*sin(2*d*x^(1/3) + 2*c) + (a^2 + b^2)*sin(2*d*x^(1/3) + 2*c)^2 + a^2 + b^2 + 2*(a^2 - b^2)*cos(2*d*x^(1/3) + 2*c))/(a^2 + b^2)) + (3*a^2*b + 3*I*a*b^2 + 3*(a^2*b - I*a*b^2)*cos(2*d*x^(1/3) + 2*c) + (3*I*a^2*b + 3*a*b^2)*sin(2*d*x^(1/3) + 2*c))*polylog(3, (I*a + b)*e^(2*I*d*x^(1/3) + 2*I*c)/(-I*a + b)) + ((I*a^3 + 3*a^2*b - 3*I*a*b^2 - b^3)*(d*x^(1/3) + c)^3 + (6*a*b^2 - 6*I*b^3 + (-3*I*a^3 - 9*a^2*b + 9*I*a*b^2 + 3*b^3)*c)*(d*x^(1/3) + c)^2 - 12*(a*b^2 - I*b^3)*(d*x^(1/3) + c)*c)*sin(2*d*x^(1/3) + 2*c))/(3*a^5 + 3*I*a^4*b + 6*a^3*b^2 + 6*I*a^2*b^3 + 3*a*b^4 + 3*I*b^5 + (3*a^5 - 3*I*a^4*b + 6*a^3*b^2 - 6*I*a^2*b^3 + 3*a*b^4 - 3*I*b^5)*cos(2*d*x^(1/3) + 2*c) + (3*I*a^5 + 3*a^4*b + 6*I*a^3*b^2 + 6*a^2*b^3 + 3*I*a*b^4 + 3*b^5)*sin(2*d*x^(1/3) + 2*c)))/d^3","B",0
65,0,0,0,0.000000," ","integrate(1/x/(a+b*tan(c+d*x^(1/3)))^2,x, algorithm=""maxima"")","\frac{-2 \, {\left({\left({\left(4 \, a^{10} b^{2} + 16 \, a^{8} b^{4} + 24 \, a^{6} b^{6} + 17 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} \cos\left(2 \, c\right)^{2} + {\left(4 \, a^{10} b^{2} + 16 \, a^{8} b^{4} + 24 \, a^{6} b^{6} + 17 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} \sin\left(2 \, c\right)^{2}\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right)^{2} + {\left(a^{12} + 2 \, a^{10} b^{2} + a^{8} b^{4}\right)} d \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + {\left({\left(4 \, a^{10} b^{2} + 16 \, a^{8} b^{4} + 24 \, a^{6} b^{6} + 17 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} \cos\left(2 \, c\right)^{2} + {\left(4 \, a^{10} b^{2} + 16 \, a^{8} b^{4} + 24 \, a^{6} b^{6} + 17 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} \sin\left(2 \, c\right)^{2}\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right)^{2} + {\left(a^{12} + 2 \, a^{10} b^{2} + a^{8} b^{4}\right)} d \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} - 2 \, {\left({\left(a^{8} b^{4} + 4 \, a^{6} b^{6} + 6 \, a^{4} b^{8} + 4 \, a^{2} b^{10} + b^{12}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{11} b + 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} + 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} + a b^{11}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right) + 2 \, {\left(2 \, {\left(a^{11} b + 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} + 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} + a b^{11}\right)} \cos\left(2 \, c\right) + {\left(a^{8} b^{4} + 4 \, a^{6} b^{6} + 6 \, a^{4} b^{8} + 4 \, a^{2} b^{10} + b^{12}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right) + {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d - 2 \, {\left({\left({\left(a^{8} b^{4} + 2 \, a^{6} b^{6} + a^{4} b^{8}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right) - {\left(2 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} \cos\left(2 \, c\right) + {\left(a^{8} b^{4} + 2 \, a^{6} b^{6} + a^{4} b^{8}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right) - {\left(a^{12} + 4 \, a^{10} b^{2} + 6 \, a^{8} b^{4} + 4 \, a^{6} b^{6} + a^{4} b^{8}\right)} d\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - 2 \, {\left({\left(2 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} \cos\left(2 \, c\right) + {\left(a^{8} b^{4} + 2 \, a^{6} b^{6} + a^{4} b^{8}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right) + {\left({\left(a^{8} b^{4} + 2 \, a^{6} b^{6} + a^{4} b^{8}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right)\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} x \int \frac{2 \, {\left(a^{5} b d \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - {\left(a b^{5} \sin\left(2 \, c\right) + 2 \, {\left(a^{4} b^{2} + a^{2} b^{4}\right)} \cos\left(2 \, c\right)\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right) - {\left(a b^{5} \cos\left(2 \, c\right) - 2 \, {\left(a^{4} b^{2} + a^{2} b^{4}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right)\right)} x - {\left(a^{4} b^{2} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - {\left(b^{6} \sin\left(2 \, c\right) + 2 \, {\left(a^{3} b^{3} + a b^{5}\right)} \cos\left(2 \, c\right)\right)} \cos\left(2 \, d x^{\frac{1}{3}}\right) - {\left(b^{6} \cos\left(2 \, c\right) - 2 \, {\left(a^{3} b^{3} + a b^{5}\right)} \sin\left(2 \, c\right)\right)} \sin\left(2 \, d x^{\frac{1}{3}}\right)\right)} x^{\frac{2}{3}}}{{\left(a^{8} d \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + a^{8} d \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + {\left({\left(4 \, a^{6} b^{2} + 8 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} \cos\left(2 \, c\right)^{2} + {\left(4 \, a^{6} b^{2} + 8 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} \sin\left(2 \, c\right)^{2}\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right)^{2} + {\left({\left(4 \, a^{6} b^{2} + 8 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} \cos\left(2 \, c\right)^{2} + {\left(4 \, a^{6} b^{2} + 8 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} \sin\left(2 \, c\right)^{2}\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right)^{2} - 2 \, {\left({\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right) + 2 \, {\left(2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} \cos\left(2 \, c\right) + {\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right) + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d - 2 \, {\left({\left(a^{4} b^{4} \cos\left(2 \, c\right) - 2 \, {\left(a^{7} b + a^{5} b^{3}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right) - {\left(a^{4} b^{4} \sin\left(2 \, c\right) + 2 \, {\left(a^{7} b + a^{5} b^{3}\right)} \cos\left(2 \, c\right)\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right) - {\left(a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} d\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - 2 \, {\left({\left(a^{4} b^{4} \sin\left(2 \, c\right) + 2 \, {\left(a^{7} b + a^{5} b^{3}\right)} \cos\left(2 \, c\right)\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right) + {\left(a^{4} b^{4} \cos\left(2 \, c\right) - 2 \, {\left(a^{7} b + a^{5} b^{3}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right)\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} x^{2}}\,{d x} + {\left({\left({\left(4 \, a^{8} b^{2} + 4 \, a^{6} b^{4} - 4 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} \cos\left(2 \, c\right)^{2} + {\left(4 \, a^{8} b^{2} + 4 \, a^{6} b^{4} - 4 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} \sin\left(2 \, c\right)^{2}\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right)^{2} + {\left(a^{10} - a^{8} b^{2}\right)} d \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + {\left({\left(4 \, a^{8} b^{2} + 4 \, a^{6} b^{4} - 4 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} \cos\left(2 \, c\right)^{2} + {\left(4 \, a^{8} b^{2} + 4 \, a^{6} b^{4} - 4 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} \sin\left(2 \, c\right)^{2}\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right)^{2} + {\left(a^{10} - a^{8} b^{2}\right)} d \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} - 2 \, {\left({\left(a^{6} b^{4} + a^{4} b^{6} - a^{2} b^{8} - b^{10}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{9} b + 2 \, a^{7} b^{3} - 2 \, a^{3} b^{7} - a b^{9}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right) + 2 \, {\left(2 \, {\left(a^{9} b + 2 \, a^{7} b^{3} - 2 \, a^{3} b^{7} - a b^{9}\right)} \cos\left(2 \, c\right) + {\left(a^{6} b^{4} + a^{4} b^{6} - a^{2} b^{8} - b^{10}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right) + {\left(a^{10} + 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} d - 2 \, {\left({\left({\left(a^{6} b^{4} - a^{4} b^{6}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{9} b - a^{5} b^{5}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right) - {\left(2 \, {\left(a^{9} b - a^{5} b^{5}\right)} \cos\left(2 \, c\right) + {\left(a^{6} b^{4} - a^{4} b^{6}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right) - {\left(a^{10} + a^{8} b^{2} - a^{6} b^{4} - a^{4} b^{6}\right)} d\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - 2 \, {\left({\left(2 \, {\left(a^{9} b - a^{5} b^{5}\right)} \cos\left(2 \, c\right) + {\left(a^{6} b^{4} - a^{4} b^{6}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right) + {\left({\left(a^{6} b^{4} - a^{4} b^{6}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{9} b - a^{5} b^{5}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right)\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} x \log\left(x\right) - 6 \, {\left({\left(2 \, {\left(a^{7} b^{3} + 3 \, a^{5} b^{5} + 3 \, a^{3} b^{7} + a b^{9}\right)} \cos\left(2 \, c\right) + {\left(a^{4} b^{6} + 2 \, a^{2} b^{8} + b^{10}\right)} \sin\left(2 \, c\right)\right)} \cos\left(2 \, d x^{\frac{1}{3}}\right) + {\left({\left(a^{4} b^{6} + 2 \, a^{2} b^{8} + b^{10}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{7} b^{3} + 3 \, a^{5} b^{5} + 3 \, a^{3} b^{7} + a b^{9}\right)} \sin\left(2 \, c\right)\right)} \sin\left(2 \, d x^{\frac{1}{3}}\right) - {\left(a^{8} b^{2} + 2 \, a^{6} b^{4} + a^{4} b^{6}\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} x^{\frac{2}{3}}}{{\left({\left({\left(4 \, a^{10} b^{2} + 16 \, a^{8} b^{4} + 24 \, a^{6} b^{6} + 17 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} \cos\left(2 \, c\right)^{2} + {\left(4 \, a^{10} b^{2} + 16 \, a^{8} b^{4} + 24 \, a^{6} b^{6} + 17 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} \sin\left(2 \, c\right)^{2}\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right)^{2} + {\left(a^{12} + 2 \, a^{10} b^{2} + a^{8} b^{4}\right)} d \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + {\left({\left(4 \, a^{10} b^{2} + 16 \, a^{8} b^{4} + 24 \, a^{6} b^{6} + 17 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} \cos\left(2 \, c\right)^{2} + {\left(4 \, a^{10} b^{2} + 16 \, a^{8} b^{4} + 24 \, a^{6} b^{6} + 17 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} \sin\left(2 \, c\right)^{2}\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right)^{2} + {\left(a^{12} + 2 \, a^{10} b^{2} + a^{8} b^{4}\right)} d \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} - 2 \, {\left({\left(a^{8} b^{4} + 4 \, a^{6} b^{6} + 6 \, a^{4} b^{8} + 4 \, a^{2} b^{10} + b^{12}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{11} b + 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} + 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} + a b^{11}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right) + 2 \, {\left(2 \, {\left(a^{11} b + 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} + 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} + a b^{11}\right)} \cos\left(2 \, c\right) + {\left(a^{8} b^{4} + 4 \, a^{6} b^{6} + 6 \, a^{4} b^{8} + 4 \, a^{2} b^{10} + b^{12}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right) + {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d - 2 \, {\left({\left({\left(a^{8} b^{4} + 2 \, a^{6} b^{6} + a^{4} b^{8}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right) - {\left(2 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} \cos\left(2 \, c\right) + {\left(a^{8} b^{4} + 2 \, a^{6} b^{6} + a^{4} b^{8}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right) - {\left(a^{12} + 4 \, a^{10} b^{2} + 6 \, a^{8} b^{4} + 4 \, a^{6} b^{6} + a^{4} b^{8}\right)} d\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - 2 \, {\left({\left(2 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} \cos\left(2 \, c\right) + {\left(a^{8} b^{4} + 2 \, a^{6} b^{6} + a^{4} b^{8}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right) + {\left({\left(a^{8} b^{4} + 2 \, a^{6} b^{6} + a^{4} b^{8}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right)\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} x}"," ",0,"((((4*a^10*b^2 + 16*a^8*b^4 + 24*a^6*b^6 + 17*a^4*b^8 + 6*a^2*b^10 + b^12)*cos(2*c)^2 + (4*a^10*b^2 + 16*a^8*b^4 + 24*a^6*b^6 + 17*a^4*b^8 + 6*a^2*b^10 + b^12)*sin(2*c)^2)*d*cos(2*d*x^(1/3))^2 + (a^12 + 2*a^10*b^2 + a^8*b^4)*d*cos(2*d*x^(1/3) + 2*c)^2 + ((4*a^10*b^2 + 16*a^8*b^4 + 24*a^6*b^6 + 17*a^4*b^8 + 6*a^2*b^10 + b^12)*cos(2*c)^2 + (4*a^10*b^2 + 16*a^8*b^4 + 24*a^6*b^6 + 17*a^4*b^8 + 6*a^2*b^10 + b^12)*sin(2*c)^2)*d*sin(2*d*x^(1/3))^2 + (a^12 + 2*a^10*b^2 + a^8*b^4)*d*sin(2*d*x^(1/3) + 2*c)^2 - 2*((a^8*b^4 + 4*a^6*b^6 + 6*a^4*b^8 + 4*a^2*b^10 + b^12)*cos(2*c) - 2*(a^11*b + 5*a^9*b^3 + 10*a^7*b^5 + 10*a^5*b^7 + 5*a^3*b^9 + a*b^11)*sin(2*c))*d*cos(2*d*x^(1/3)) + 2*(2*(a^11*b + 5*a^9*b^3 + 10*a^7*b^5 + 10*a^5*b^7 + 5*a^3*b^9 + a*b^11)*cos(2*c) + (a^8*b^4 + 4*a^6*b^6 + 6*a^4*b^8 + 4*a^2*b^10 + b^12)*sin(2*c))*d*sin(2*d*x^(1/3)) + (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d - 2*(((a^8*b^4 + 2*a^6*b^6 + a^4*b^8)*cos(2*c) - 2*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*sin(2*c))*d*cos(2*d*x^(1/3)) - (2*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*cos(2*c) + (a^8*b^4 + 2*a^6*b^6 + a^4*b^8)*sin(2*c))*d*sin(2*d*x^(1/3)) - (a^12 + 4*a^10*b^2 + 6*a^8*b^4 + 4*a^6*b^6 + a^4*b^8)*d)*cos(2*d*x^(1/3) + 2*c) - 2*((2*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*cos(2*c) + (a^8*b^4 + 2*a^6*b^6 + a^4*b^8)*sin(2*c))*d*cos(2*d*x^(1/3)) + ((a^8*b^4 + 2*a^6*b^6 + a^4*b^8)*cos(2*c) - 2*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*sin(2*c))*d*sin(2*d*x^(1/3)))*sin(2*d*x^(1/3) + 2*c))*x*integrate(-2*(2*(a^5*b*d*sin(2*d*x^(1/3) + 2*c) - (a*b^5*sin(2*c) + 2*(a^4*b^2 + a^2*b^4)*cos(2*c))*d*cos(2*d*x^(1/3)) - (a*b^5*cos(2*c) - 2*(a^4*b^2 + a^2*b^4)*sin(2*c))*d*sin(2*d*x^(1/3)))*x - (a^4*b^2*sin(2*d*x^(1/3) + 2*c) - (b^6*sin(2*c) + 2*(a^3*b^3 + a*b^5)*cos(2*c))*cos(2*d*x^(1/3)) - (b^6*cos(2*c) - 2*(a^3*b^3 + a*b^5)*sin(2*c))*sin(2*d*x^(1/3)))*x^(2/3))/((a^8*d*cos(2*d*x^(1/3) + 2*c)^2 + a^8*d*sin(2*d*x^(1/3) + 2*c)^2 + ((4*a^6*b^2 + 8*a^4*b^4 + 4*a^2*b^6 + b^8)*cos(2*c)^2 + (4*a^6*b^2 + 8*a^4*b^4 + 4*a^2*b^6 + b^8)*sin(2*c)^2)*d*cos(2*d*x^(1/3))^2 + ((4*a^6*b^2 + 8*a^4*b^4 + 4*a^2*b^6 + b^8)*cos(2*c)^2 + (4*a^6*b^2 + 8*a^4*b^4 + 4*a^2*b^6 + b^8)*sin(2*c)^2)*d*sin(2*d*x^(1/3))^2 - 2*((a^4*b^4 + 2*a^2*b^6 + b^8)*cos(2*c) - 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*sin(2*c))*d*cos(2*d*x^(1/3)) + 2*(2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*cos(2*c) + (a^4*b^4 + 2*a^2*b^6 + b^8)*sin(2*c))*d*sin(2*d*x^(1/3)) + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d - 2*((a^4*b^4*cos(2*c) - 2*(a^7*b + a^5*b^3)*sin(2*c))*d*cos(2*d*x^(1/3)) - (a^4*b^4*sin(2*c) + 2*(a^7*b + a^5*b^3)*cos(2*c))*d*sin(2*d*x^(1/3)) - (a^8 + 2*a^6*b^2 + a^4*b^4)*d)*cos(2*d*x^(1/3) + 2*c) - 2*((a^4*b^4*sin(2*c) + 2*(a^7*b + a^5*b^3)*cos(2*c))*d*cos(2*d*x^(1/3)) + (a^4*b^4*cos(2*c) - 2*(a^7*b + a^5*b^3)*sin(2*c))*d*sin(2*d*x^(1/3)))*sin(2*d*x^(1/3) + 2*c))*x^2), x) + (((4*a^8*b^2 + 4*a^6*b^4 - 4*a^4*b^6 - 3*a^2*b^8 - b^10)*cos(2*c)^2 + (4*a^8*b^2 + 4*a^6*b^4 - 4*a^4*b^6 - 3*a^2*b^8 - b^10)*sin(2*c)^2)*d*cos(2*d*x^(1/3))^2 + (a^10 - a^8*b^2)*d*cos(2*d*x^(1/3) + 2*c)^2 + ((4*a^8*b^2 + 4*a^6*b^4 - 4*a^4*b^6 - 3*a^2*b^8 - b^10)*cos(2*c)^2 + (4*a^8*b^2 + 4*a^6*b^4 - 4*a^4*b^6 - 3*a^2*b^8 - b^10)*sin(2*c)^2)*d*sin(2*d*x^(1/3))^2 + (a^10 - a^8*b^2)*d*sin(2*d*x^(1/3) + 2*c)^2 - 2*((a^6*b^4 + a^4*b^6 - a^2*b^8 - b^10)*cos(2*c) - 2*(a^9*b + 2*a^7*b^3 - 2*a^3*b^7 - a*b^9)*sin(2*c))*d*cos(2*d*x^(1/3)) + 2*(2*(a^9*b + 2*a^7*b^3 - 2*a^3*b^7 - a*b^9)*cos(2*c) + (a^6*b^4 + a^4*b^6 - a^2*b^8 - b^10)*sin(2*c))*d*sin(2*d*x^(1/3)) + (a^10 + 3*a^8*b^2 + 2*a^6*b^4 - 2*a^4*b^6 - 3*a^2*b^8 - b^10)*d - 2*(((a^6*b^4 - a^4*b^6)*cos(2*c) - 2*(a^9*b - a^5*b^5)*sin(2*c))*d*cos(2*d*x^(1/3)) - (2*(a^9*b - a^5*b^5)*cos(2*c) + (a^6*b^4 - a^4*b^6)*sin(2*c))*d*sin(2*d*x^(1/3)) - (a^10 + a^8*b^2 - a^6*b^4 - a^4*b^6)*d)*cos(2*d*x^(1/3) + 2*c) - 2*((2*(a^9*b - a^5*b^5)*cos(2*c) + (a^6*b^4 - a^4*b^6)*sin(2*c))*d*cos(2*d*x^(1/3)) + ((a^6*b^4 - a^4*b^6)*cos(2*c) - 2*(a^9*b - a^5*b^5)*sin(2*c))*d*sin(2*d*x^(1/3)))*sin(2*d*x^(1/3) + 2*c))*x*log(x) - 6*((2*(a^7*b^3 + 3*a^5*b^5 + 3*a^3*b^7 + a*b^9)*cos(2*c) + (a^4*b^6 + 2*a^2*b^8 + b^10)*sin(2*c))*cos(2*d*x^(1/3)) + ((a^4*b^6 + 2*a^2*b^8 + b^10)*cos(2*c) - 2*(a^7*b^3 + 3*a^5*b^5 + 3*a^3*b^7 + a*b^9)*sin(2*c))*sin(2*d*x^(1/3)) - (a^8*b^2 + 2*a^6*b^4 + a^4*b^6)*sin(2*d*x^(1/3) + 2*c))*x^(2/3))/((((4*a^10*b^2 + 16*a^8*b^4 + 24*a^6*b^6 + 17*a^4*b^8 + 6*a^2*b^10 + b^12)*cos(2*c)^2 + (4*a^10*b^2 + 16*a^8*b^4 + 24*a^6*b^6 + 17*a^4*b^8 + 6*a^2*b^10 + b^12)*sin(2*c)^2)*d*cos(2*d*x^(1/3))^2 + (a^12 + 2*a^10*b^2 + a^8*b^4)*d*cos(2*d*x^(1/3) + 2*c)^2 + ((4*a^10*b^2 + 16*a^8*b^4 + 24*a^6*b^6 + 17*a^4*b^8 + 6*a^2*b^10 + b^12)*cos(2*c)^2 + (4*a^10*b^2 + 16*a^8*b^4 + 24*a^6*b^6 + 17*a^4*b^8 + 6*a^2*b^10 + b^12)*sin(2*c)^2)*d*sin(2*d*x^(1/3))^2 + (a^12 + 2*a^10*b^2 + a^8*b^4)*d*sin(2*d*x^(1/3) + 2*c)^2 - 2*((a^8*b^4 + 4*a^6*b^6 + 6*a^4*b^8 + 4*a^2*b^10 + b^12)*cos(2*c) - 2*(a^11*b + 5*a^9*b^3 + 10*a^7*b^5 + 10*a^5*b^7 + 5*a^3*b^9 + a*b^11)*sin(2*c))*d*cos(2*d*x^(1/3)) + 2*(2*(a^11*b + 5*a^9*b^3 + 10*a^7*b^5 + 10*a^5*b^7 + 5*a^3*b^9 + a*b^11)*cos(2*c) + (a^8*b^4 + 4*a^6*b^6 + 6*a^4*b^8 + 4*a^2*b^10 + b^12)*sin(2*c))*d*sin(2*d*x^(1/3)) + (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d - 2*(((a^8*b^4 + 2*a^6*b^6 + a^4*b^8)*cos(2*c) - 2*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*sin(2*c))*d*cos(2*d*x^(1/3)) - (2*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*cos(2*c) + (a^8*b^4 + 2*a^6*b^6 + a^4*b^8)*sin(2*c))*d*sin(2*d*x^(1/3)) - (a^12 + 4*a^10*b^2 + 6*a^8*b^4 + 4*a^6*b^6 + a^4*b^8)*d)*cos(2*d*x^(1/3) + 2*c) - 2*((2*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*cos(2*c) + (a^8*b^4 + 2*a^6*b^6 + a^4*b^8)*sin(2*c))*d*cos(2*d*x^(1/3)) + ((a^8*b^4 + 2*a^6*b^6 + a^4*b^8)*cos(2*c) - 2*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*sin(2*c))*d*sin(2*d*x^(1/3)))*sin(2*d*x^(1/3) + 2*c))*x)","F",0
66,0,0,0,0.000000," ","integrate(1/x^2/(a+b*tan(c+d*x^(1/3)))^2,x, algorithm=""maxima"")","\frac{-4 \, {\left(a^{8} d \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + a^{8} d \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + {\left({\left(4 \, a^{6} b^{2} + 8 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} \cos\left(2 \, c\right)^{2} + {\left(4 \, a^{6} b^{2} + 8 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} \sin\left(2 \, c\right)^{2}\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right)^{2} + {\left({\left(4 \, a^{6} b^{2} + 8 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} \cos\left(2 \, c\right)^{2} + {\left(4 \, a^{6} b^{2} + 8 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} \sin\left(2 \, c\right)^{2}\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right)^{2} - 2 \, {\left({\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right) + 2 \, {\left(2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} \cos\left(2 \, c\right) + {\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right) + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d - 2 \, {\left({\left(a^{4} b^{4} \cos\left(2 \, c\right) - 2 \, {\left(a^{7} b + a^{5} b^{3}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right) - {\left(a^{4} b^{4} \sin\left(2 \, c\right) + 2 \, {\left(a^{7} b + a^{5} b^{3}\right)} \cos\left(2 \, c\right)\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right) - {\left(a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} d\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - 2 \, {\left({\left(a^{4} b^{4} \sin\left(2 \, c\right) + 2 \, {\left(a^{7} b + a^{5} b^{3}\right)} \cos\left(2 \, c\right)\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right) + {\left(a^{4} b^{4} \cos\left(2 \, c\right) - 2 \, {\left(a^{7} b + a^{5} b^{3}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right)\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} x^{2} \int \frac{{\left(a^{5} b d \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - {\left(a b^{5} \sin\left(2 \, c\right) + 2 \, {\left(a^{4} b^{2} + a^{2} b^{4}\right)} \cos\left(2 \, c\right)\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right) - {\left(a b^{5} \cos\left(2 \, c\right) - 2 \, {\left(a^{4} b^{2} + a^{2} b^{4}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right)\right)} x - 2 \, {\left(a^{4} b^{2} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - {\left(b^{6} \sin\left(2 \, c\right) + 2 \, {\left(a^{3} b^{3} + a b^{5}\right)} \cos\left(2 \, c\right)\right)} \cos\left(2 \, d x^{\frac{1}{3}}\right) - {\left(b^{6} \cos\left(2 \, c\right) - 2 \, {\left(a^{3} b^{3} + a b^{5}\right)} \sin\left(2 \, c\right)\right)} \sin\left(2 \, d x^{\frac{1}{3}}\right)\right)} x^{\frac{2}{3}}}{{\left(a^{8} d \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + a^{8} d \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + {\left({\left(4 \, a^{6} b^{2} + 8 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} \cos\left(2 \, c\right)^{2} + {\left(4 \, a^{6} b^{2} + 8 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} \sin\left(2 \, c\right)^{2}\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right)^{2} + {\left({\left(4 \, a^{6} b^{2} + 8 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} \cos\left(2 \, c\right)^{2} + {\left(4 \, a^{6} b^{2} + 8 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} \sin\left(2 \, c\right)^{2}\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right)^{2} - 2 \, {\left({\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right) + 2 \, {\left(2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} \cos\left(2 \, c\right) + {\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right) + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d - 2 \, {\left({\left(a^{4} b^{4} \cos\left(2 \, c\right) - 2 \, {\left(a^{7} b + a^{5} b^{3}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right) - {\left(a^{4} b^{4} \sin\left(2 \, c\right) + 2 \, {\left(a^{7} b + a^{5} b^{3}\right)} \cos\left(2 \, c\right)\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right) - {\left(a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} d\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - 2 \, {\left({\left(a^{4} b^{4} \sin\left(2 \, c\right) + 2 \, {\left(a^{7} b + a^{5} b^{3}\right)} \cos\left(2 \, c\right)\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right) + {\left(a^{4} b^{4} \cos\left(2 \, c\right) - 2 \, {\left(a^{7} b + a^{5} b^{3}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right)\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} x^{3}}\,{d x} - {\left({\left(a^{6} + a^{4} b^{2}\right)} d \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + {\left(a^{6} + a^{4} b^{2}\right)} d \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} - {\left({\left(4 \, a^{4} b^{2} + 5 \, a^{2} b^{4} - b^{6}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{5} b - 2 \, a b^{5}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right) + {\left(2 \, {\left(a^{5} b - 2 \, a b^{5}\right)} \cos\left(2 \, c\right) + {\left(4 \, a^{4} b^{2} + 5 \, a^{2} b^{4} - b^{6}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right) + {\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} d - {\left({\left({\left(a^{2} b^{4} + b^{6}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right) - {\left(2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(2 \, c\right) + {\left(a^{2} b^{4} + b^{6}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right) - {\left(2 \, a^{6} + 2 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) + {\left(2 \, a^{5} b d - {\left(2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(2 \, c\right) + {\left(a^{2} b^{4} + b^{6}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right) - {\left({\left(a^{2} b^{4} + b^{6}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right)\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} x + 6 \, {\left(a^{4} b^{2} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - {\left(b^{6} \sin\left(2 \, c\right) + 2 \, {\left(a^{3} b^{3} + a b^{5}\right)} \cos\left(2 \, c\right)\right)} \cos\left(2 \, d x^{\frac{1}{3}}\right) - {\left(b^{6} \cos\left(2 \, c\right) - 2 \, {\left(a^{3} b^{3} + a b^{5}\right)} \sin\left(2 \, c\right)\right)} \sin\left(2 \, d x^{\frac{1}{3}}\right)\right)} x^{\frac{2}{3}}}{{\left(a^{8} d \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + a^{8} d \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)^{2} + {\left({\left(4 \, a^{6} b^{2} + 8 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} \cos\left(2 \, c\right)^{2} + {\left(4 \, a^{6} b^{2} + 8 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} \sin\left(2 \, c\right)^{2}\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right)^{2} + {\left({\left(4 \, a^{6} b^{2} + 8 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} \cos\left(2 \, c\right)^{2} + {\left(4 \, a^{6} b^{2} + 8 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} \sin\left(2 \, c\right)^{2}\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right)^{2} - 2 \, {\left({\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} \cos\left(2 \, c\right) - 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right) + 2 \, {\left(2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} \cos\left(2 \, c\right) + {\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right) + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d - 2 \, {\left({\left(a^{4} b^{4} \cos\left(2 \, c\right) - 2 \, {\left(a^{7} b + a^{5} b^{3}\right)} \sin\left(2 \, c\right)\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right) - {\left(a^{4} b^{4} \sin\left(2 \, c\right) + 2 \, {\left(a^{7} b + a^{5} b^{3}\right)} \cos\left(2 \, c\right)\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right) - {\left(a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} d\right)} \cos\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right) - 2 \, {\left({\left(a^{4} b^{4} \sin\left(2 \, c\right) + 2 \, {\left(a^{7} b + a^{5} b^{3}\right)} \cos\left(2 \, c\right)\right)} d \cos\left(2 \, d x^{\frac{1}{3}}\right) + {\left(a^{4} b^{4} \cos\left(2 \, c\right) - 2 \, {\left(a^{7} b + a^{5} b^{3}\right)} \sin\left(2 \, c\right)\right)} d \sin\left(2 \, d x^{\frac{1}{3}}\right)\right)} \sin\left(2 \, d x^{\frac{1}{3}} + 2 \, c\right)\right)} x^{2}}"," ",0,"((a^8*d*cos(2*d*x^(1/3) + 2*c)^2 + a^8*d*sin(2*d*x^(1/3) + 2*c)^2 + ((4*a^6*b^2 + 8*a^4*b^4 + 4*a^2*b^6 + b^8)*cos(2*c)^2 + (4*a^6*b^2 + 8*a^4*b^4 + 4*a^2*b^6 + b^8)*sin(2*c)^2)*d*cos(2*d*x^(1/3))^2 + ((4*a^6*b^2 + 8*a^4*b^4 + 4*a^2*b^6 + b^8)*cos(2*c)^2 + (4*a^6*b^2 + 8*a^4*b^4 + 4*a^2*b^6 + b^8)*sin(2*c)^2)*d*sin(2*d*x^(1/3))^2 - 2*((a^4*b^4 + 2*a^2*b^6 + b^8)*cos(2*c) - 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*sin(2*c))*d*cos(2*d*x^(1/3)) + 2*(2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*cos(2*c) + (a^4*b^4 + 2*a^2*b^6 + b^8)*sin(2*c))*d*sin(2*d*x^(1/3)) + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d - 2*((a^4*b^4*cos(2*c) - 2*(a^7*b + a^5*b^3)*sin(2*c))*d*cos(2*d*x^(1/3)) - (a^4*b^4*sin(2*c) + 2*(a^7*b + a^5*b^3)*cos(2*c))*d*sin(2*d*x^(1/3)) - (a^8 + 2*a^6*b^2 + a^4*b^4)*d)*cos(2*d*x^(1/3) + 2*c) - 2*((a^4*b^4*sin(2*c) + 2*(a^7*b + a^5*b^3)*cos(2*c))*d*cos(2*d*x^(1/3)) + (a^4*b^4*cos(2*c) - 2*(a^7*b + a^5*b^3)*sin(2*c))*d*sin(2*d*x^(1/3)))*sin(2*d*x^(1/3) + 2*c))*x^2*integrate(-4*((a^5*b*d*sin(2*d*x^(1/3) + 2*c) - (a*b^5*sin(2*c) + 2*(a^4*b^2 + a^2*b^4)*cos(2*c))*d*cos(2*d*x^(1/3)) - (a*b^5*cos(2*c) - 2*(a^4*b^2 + a^2*b^4)*sin(2*c))*d*sin(2*d*x^(1/3)))*x - 2*(a^4*b^2*sin(2*d*x^(1/3) + 2*c) - (b^6*sin(2*c) + 2*(a^3*b^3 + a*b^5)*cos(2*c))*cos(2*d*x^(1/3)) - (b^6*cos(2*c) - 2*(a^3*b^3 + a*b^5)*sin(2*c))*sin(2*d*x^(1/3)))*x^(2/3))/((a^8*d*cos(2*d*x^(1/3) + 2*c)^2 + a^8*d*sin(2*d*x^(1/3) + 2*c)^2 + ((4*a^6*b^2 + 8*a^4*b^4 + 4*a^2*b^6 + b^8)*cos(2*c)^2 + (4*a^6*b^2 + 8*a^4*b^4 + 4*a^2*b^6 + b^8)*sin(2*c)^2)*d*cos(2*d*x^(1/3))^2 + ((4*a^6*b^2 + 8*a^4*b^4 + 4*a^2*b^6 + b^8)*cos(2*c)^2 + (4*a^6*b^2 + 8*a^4*b^4 + 4*a^2*b^6 + b^8)*sin(2*c)^2)*d*sin(2*d*x^(1/3))^2 - 2*((a^4*b^4 + 2*a^2*b^6 + b^8)*cos(2*c) - 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*sin(2*c))*d*cos(2*d*x^(1/3)) + 2*(2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*cos(2*c) + (a^4*b^4 + 2*a^2*b^6 + b^8)*sin(2*c))*d*sin(2*d*x^(1/3)) + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d - 2*((a^4*b^4*cos(2*c) - 2*(a^7*b + a^5*b^3)*sin(2*c))*d*cos(2*d*x^(1/3)) - (a^4*b^4*sin(2*c) + 2*(a^7*b + a^5*b^3)*cos(2*c))*d*sin(2*d*x^(1/3)) - (a^8 + 2*a^6*b^2 + a^4*b^4)*d)*cos(2*d*x^(1/3) + 2*c) - 2*((a^4*b^4*sin(2*c) + 2*(a^7*b + a^5*b^3)*cos(2*c))*d*cos(2*d*x^(1/3)) + (a^4*b^4*cos(2*c) - 2*(a^7*b + a^5*b^3)*sin(2*c))*d*sin(2*d*x^(1/3)))*sin(2*d*x^(1/3) + 2*c))*x^3), x) - ((a^6 + a^4*b^2)*d*cos(2*d*x^(1/3) + 2*c)^2 + (a^6 + a^4*b^2)*d*sin(2*d*x^(1/3) + 2*c)^2 - ((4*a^4*b^2 + 5*a^2*b^4 - b^6)*cos(2*c) - 2*(a^5*b - 2*a*b^5)*sin(2*c))*d*cos(2*d*x^(1/3)) + (2*(a^5*b - 2*a*b^5)*cos(2*c) + (4*a^4*b^2 + 5*a^2*b^4 - b^6)*sin(2*c))*d*sin(2*d*x^(1/3)) + (a^6 + a^4*b^2 - a^2*b^4 - b^6)*d - (((a^2*b^4 + b^6)*cos(2*c) - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*sin(2*c))*d*cos(2*d*x^(1/3)) - (2*(a^5*b + 2*a^3*b^3 + a*b^5)*cos(2*c) + (a^2*b^4 + b^6)*sin(2*c))*d*sin(2*d*x^(1/3)) - (2*a^6 + 2*a^4*b^2 + 3*a^2*b^4 + b^6)*d)*cos(2*d*x^(1/3) + 2*c) + (2*a^5*b*d - (2*(a^5*b + 2*a^3*b^3 + a*b^5)*cos(2*c) + (a^2*b^4 + b^6)*sin(2*c))*d*cos(2*d*x^(1/3)) - ((a^2*b^4 + b^6)*cos(2*c) - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*sin(2*c))*d*sin(2*d*x^(1/3)))*sin(2*d*x^(1/3) + 2*c))*x + 6*(a^4*b^2*sin(2*d*x^(1/3) + 2*c) - (b^6*sin(2*c) + 2*(a^3*b^3 + a*b^5)*cos(2*c))*cos(2*d*x^(1/3)) - (b^6*cos(2*c) - 2*(a^3*b^3 + a*b^5)*sin(2*c))*sin(2*d*x^(1/3)))*x^(2/3))/((a^8*d*cos(2*d*x^(1/3) + 2*c)^2 + a^8*d*sin(2*d*x^(1/3) + 2*c)^2 + ((4*a^6*b^2 + 8*a^4*b^4 + 4*a^2*b^6 + b^8)*cos(2*c)^2 + (4*a^6*b^2 + 8*a^4*b^4 + 4*a^2*b^6 + b^8)*sin(2*c)^2)*d*cos(2*d*x^(1/3))^2 + ((4*a^6*b^2 + 8*a^4*b^4 + 4*a^2*b^6 + b^8)*cos(2*c)^2 + (4*a^6*b^2 + 8*a^4*b^4 + 4*a^2*b^6 + b^8)*sin(2*c)^2)*d*sin(2*d*x^(1/3))^2 - 2*((a^4*b^4 + 2*a^2*b^6 + b^8)*cos(2*c) - 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*sin(2*c))*d*cos(2*d*x^(1/3)) + 2*(2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*cos(2*c) + (a^4*b^4 + 2*a^2*b^6 + b^8)*sin(2*c))*d*sin(2*d*x^(1/3)) + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d - 2*((a^4*b^4*cos(2*c) - 2*(a^7*b + a^5*b^3)*sin(2*c))*d*cos(2*d*x^(1/3)) - (a^4*b^4*sin(2*c) + 2*(a^7*b + a^5*b^3)*cos(2*c))*d*sin(2*d*x^(1/3)) - (a^8 + 2*a^6*b^2 + a^4*b^4)*d)*cos(2*d*x^(1/3) + 2*c) - 2*((a^4*b^4*sin(2*c) + 2*(a^7*b + a^5*b^3)*cos(2*c))*d*cos(2*d*x^(1/3)) + (a^4*b^4*cos(2*c) - 2*(a^7*b + a^5*b^3)*sin(2*c))*d*sin(2*d*x^(1/3)))*sin(2*d*x^(1/3) + 2*c))*x^2)","F",0
